Let's see who passed intro algebra.
No calculators or wolfram alpha.
Go.
>>679257422
(x-1)^0.5 + 7 = 2
(x-1)^0.5 = -5
square root is defined to always be >= 0 so no solution exists
>>679257422
Sqrt(x-1) + 7 = 2
Sqrt(x-1) = -5
x-1 = 25
x = 26
However, this solution does not work when checking.
sqrt(26 - 1) + 7 = 2
sqrt(25) + 7 = 2
5 + 7 = 2
12 =/= 2
Therefore there is no solution
26 no problem fagoots
>>679257422
x = 26
-7 on both sides square both sides to remove square root, plus one, simple math
videogames
26? Fuck if i know
>>679257687
many thanks, anon ... i was struggling to come up with an answer because i couldn't fathom any square root that would equal a negative number (not op)
82..
>>679257422
Twenty-six
>>679257907
Sqrt(25)=5 and -5
>>679257907
This is correct. Squaring does not always preserve equality.
Gotta check dat answer; 26 doesn't work.
>>679257907
You were close. Remember that the sqrt gives positive and negative 5 as the answers. Negative 5 is the true solution.
all you fags saying 26 are just complete faggots go back to middle school
>>679258386
Mean't to say square root does not always preserve equality
>>679257422
x=-2
>>679258313
incorrect.
the sqrt function/operation is always defined to be positive. you can test this yourself by graphing it on a graphing calculator.
However, it is true that the solution set for x^2 = 25 is 5 and -5
>>679257422
No solution for x in IR
>>679257915
>>679257923
>>679258004
>>679258158
sqrt(26-1)+7 =/= 2
Fuckers
>>679257687
umm no. -1^.5 = j
where j is imaginary
>>679258386
You have to use a plus/minus, there are two answers. Not one.
now let's try a geography question, and don't look at a map:
what continent is due south of greenland?
>>679258750
>-1^.5 = j
what the fuck?
it's sqrt(-1) = i
i is imaginary, it's the first fucking letter. J? what the fuck?
It's 26. Square root as inverse of square has two solutions, positive and negative. Usually square root symbol means positive, but if you're hinging on that then fuck this question.
>>679258814
S.America
>>679258952
>fuck this question
non-mathing autismo detected
>>679258814
Every fucking continent
>>679258904
j is used everywhere in engineering. i isnt used
>>679258806
There is only one solution because the original equation's highest power is 1.
26i
i represents (sqrt) -1 because a typical square root can never equal a negative, it is an imaginary number
>>679257907
and for anyone who said no solution
>>679259025
very good. this surprised me when i realized it
fuck you and your math bitch
>>679258593
Always? It's been a while since I took math, but I don't remember that rule.
>>679257422
x - 1 = 25
x = 26
>>679259273
said the autist
26
>>679259273
correction, Square root of X-1 = -25
x=26
Take the negative root when you sqrt 25
>>679257422
nigga im a math major the answer is x=24
>>679259495
>nigga im a math major
>>679259205
It's not a rule, it's a property.
While very similar, if we were to include both positive and negative solutions for an equation of the form: sqrt(x) = c, then we would be violating the injectivity (or one-to-one -ness) of the sqrt function, thus making it not a function.
ie. including negatives will violate the vertical line test.
>>679259495
or 26 depending on the +/-
>>679257687
The square root of a negative number has both a real and imaginary portion. Go back to 10th grad fag.
Source: Theoretical computer science grad student.
>>679257422
Always check answers.
>>679259495
Maybe Art history is more your speed
>>679257422
>>679259495
>nigga
>math major
x = +/- 25 + 1
>>679259122
ya the sqrt(26i-1)=/= -5
the original case has no solution simply because you cant sub the answer back in
>>679259745
-26,24
>niggers calling them "imaginary" numbers
>>679259814
Can't sub the answer back in? how so? with the use of imaginary numbers there never is 'technically' an answer, if that's what you mean
>>679259081
No, it's square root on one side, or squared on the other. The highest order is two.
>>679259956
fuck off jon, ill push your ass down a hill you fat cunt
>>679257422
Now I could be just a moron, but could someone enlighten me as to why this solution may be wrong:
SQRT (x-1) = 9
Square both sides, removes the sqrt symbol, giving x-1 = 81, Then add 1 to both sides giving x=82. Am I retarded?
√(x-1)+7=2
√(x-1)=-5
square both sides
x-1=25
x=26
>>679260205
I am retarded. I just added a number I should subtract. TIME TO AN HERO
>>679260205
subtract 7 from 2, not add.
it makes -5, not 9
>>679260089
Incorrect. Again, including both positive and negative solutions violates injectivity
>>679260205
good idea. messed up 1st step. no idea why you thought to add the 7 and 2, while you should have subtracted because of opposite sides
>>679260205
But yeah, redid it and got 26. Squaring -5 is 25, add 1. Straightforward right?
>>679260362
What does the arrow mean in algebra again?
>>679260448
as x approaches infinity.
>>679260448
I think that's trying to depict a limit
>>679260315
Redid, got 26. Sleepy.
>>679260220
-5^2 is not just 25 its + or minus 25 b/c look it up
>>679260362
>limit of f(x) equals a function of x
>limit of f(x) equals a +/-
This is literally nonsensical. Not even an "I don't get it" nonsensical, but a "This isn't how limits work" nonsensical.
>>679257422
sqrt(x - 1) = -5
So, whatever is under the radical = 25i
25i = x - 1
x = 25i + 1
it doesn't have an imaginary solution either gay boys
the square root of a complex number with a nonzero real and imaginary parts is equal to a complex number with nonzero real and imaginary parts
>>679259071
>i isn't used in engineering
Go back to high school dude
https://www.wolframalpha.com/input/?i=sqrt(x-1)%2B7%3D2+solve+for+x
>>679260967
check 'em
sqrt((25i+1) - 1) + 7 = 2
sqrt(25i) + 7 = 2
doesn't check out, bruh
>>679257422
This has no answear, b/c you cannot have a negative after you square root the x, therefore any number after zero including zero would eventually be added to 7 making (something) + 7 =|= 2
>>679260345
I'm just dropping by to say that injectivity is not a requirement of a function.
>>679260967
square both sides, not sqrt(-5)
>>679261459
In order for a relation to be a function, it must be a bijection, aka injective and surjective.
injection is essentially the vertical line test: every f(x) must have at most one x.
>>679261145
not the same fag. j is used much more often in engineering. Enjoy your liberal arts degree
>>679261411
imaginary solutions nigga
>>679257422
i never passed algebra
>>679261659
CE major. Current is pretty important. Not to mention the fact that anyone majoring in engineering has to take plenty of math classes where i is used extensively.
x=26 but if you plug it back in it breaks because sqrt(25) can be 5 and -5 at the same time.
X=-25i+1
>>679261636
I thought this wasn't a function in the sense it wasn't defined as one. It's merely an equation.
>ITT: Faggots who never passed Algebra I
>>679258814
>>679259025
Interesting point to add:
The eastern-most point of mainland Greenland is due north of mainland Africa.
>>679262025
the square root is function
but I also brushed up on my set theory, and a function does not need to be injective. my bad there.
x = 2
>>679260220
Let's try that out
√(x-1)+7=2
x=26
√(26-1)+7=2
√25+7=2
5+7=2
12=2
You fucked up
>>679260722
no it's not.
-5 x -5 =25
You're thinking of the fact that sqrt(25) has two solutions. 5 and -5
>>679257422
x = 25(i ^ 4) + 1
>>679262287
If you plug in -5 for the square rot of 25, it works fine.
>>679257422
uh...4?
>>679260064
no there is no solution that is valid
imaginary numbers are simply a method for representation but 1i=/=-1 which is what youre thinking
which is why i stated
sqrt(26i-1)=/= -5
because for the equation to be true you need y+7=2 which means sqrt(x-1)=-5 and youll never get that answer
>>679257422
>Let's see who passed intro algebra.
Ok
>>679262292
>You're thinking of the fact that sqrt(25) has two solutions. 5 and -5
-5 isn't a solution
>>679262523
It's a solution to sqrt(25)
>>679262413
You can't just choose to use one value and not the other. It doesn't work for +5, so it's not a solution.
>>679261636
I think you mean that injection is the horizontal line test: one and only one y value for each x given that f(x)=y is a relatiom mapping Set X to Set Y. The vertical line test is that f(x) multiple x's mapped to the same y. Then surjection is that every y in Set Y is mapped to a corresponding x value in Set X by f(x).
I'm pretty sure a function can exist without being bijective. Otherwise, basic functions such as polynomials and hemispheres wouldn't be considered functions, as the former is not injective and the latter is neither injective nor surjective.
At least that's what I was taught in my math classes.
>>679257422
x = 25i
You dumb shit
Guys the question is very simply "does a square root always mean positive square root." its a question of rules / conventions in math, not of arithmetic
>>679263081
test it, you nigger. it doesn't work and youre being cucked by a nigger as we speak
>>679262959
>The vertical line test is that f(x) multiple y's mapped to the same x.
Fuck, I'm tired. Probably a bad time to talk math on 4chan.
>>679258497
This is a trip. Just when I thought I was cushty for algebra, I get wronged again.
I would have said right off the bat that x=26. So the upshot of this is that squaring when you have a sqrt on one side and a -ve integer on the other does not necessarily mean that the negative disappears? Or am I being stupid?
>>679262523
5 times 5 equals 25
-5 times -5 also equals 25
thus the square root of 25 can be both 5 and -5. in this case, it's -5, and x = 26
>>679258632
sqrt(26-1)=+or-5 tho
-5+7=2
?
>>679263379
It actually has no solution
>>679263475
You have to use both 5 and -5 or it doesn't work
X= (1 + 81i^4)
>>679262012
on the right track, the negative is redundant
x = 25i + 1
thus:
sqrt(x - 1) + 7 = 2
sqrt([25i + 1] -) + 7 = 2
sqrt(25i) + 7 = 2
-5 + 7 = 2
2 = 2
>>679263853
second line should be
sqrt([25i + 1] - 1) + 7 = 2
sorry!
>>679263613
>It actually has no solution
if you don't elaborate on that, your post means literally nothing
>You have to use both 5 and -5 or it doesn't work
actually, you don't. -5 is the only one that makes the equation true so it's the only one you need to use. x = 26
>>679263803
i^4=1
>>679257422
X=26
>>679264044
sqrt(25i) =/= -5
sqrt(25i) = 5 * sqrt(i)
sqrt(i) is approx. 0.707106781 + 0.707106781 i
so that doesn't work, friend.
>>679264457
x = 26 is a valid solution
>>679264127
no REAL solution. -5 is only part of the solution for sqrt(25).
>>679264457
see
>>679264569
69 gets it
i^4 = (i^2)^2......
so would sqrt(i^4)=sqrt[(i^2)^2] = i^2
>>679264574
No it's not. There's no +/- sign in front of the sqrt.
5+7=/=2
>>679264658
it's the only part you need for x = 26 to be true
>>679257422
you dumb niggers
sqrt(x-1)+7=2
>minus 7 from both sides
sqrt(x-1)= -5
>square both sides
x-1=25
>add 1 to both sides
x=26
x = [26,-24]
there are two solutions
>>679265007
x can't be -24
>>679264569
what's the answer?
>>679258952
But in ALL mathematics it cannot happen, it is only measured in positives as a formality.
>>679260220
EXTRANEOUS SOLUTION
>thinks person is smart
>forgets that not all solutions are answers
>>679264993
actually this isnt 100% true. mah B
This solution (x=26) only exists when the function sqrt(x-1) is equal to -5. other than that no other solutions exist.
>>679259590
But isn't the vertical line test only necessary for functions? Since this is just an algebraic equation isn't it proper to account for the negative solutions as well?
This is coming from a high school AP Calc AB student so I'm no authority, just wondering. Looking into careers in mathematics.
The answer is the symbol that looks like a zero with a line through it, or not applicable.
Imaginary numbers, guise, pls.
sqrt(a)=k implies a=k^2 only for positive k
sqrt(x-1) = -5
x-1 = 25
x = 24
>>679257422
minus 7 both sides equals -5
square both sides equals x-1 = 25
add one equal 24
x= 24, done
>>679257422
Passed algebra but forgot this shit instantly, it's really fuckin retarded and useless to know in the age of computers anyway.
>>679261411
Shit is undefined
>>679266181
26* holy fuck lol
>>679266181
Nice addition skills.
>>679257422
the solution does not exist
>>679265902
or {}
>>679257687
>square root is defined to always be >= 0 so no solution exists
kill yourself
>>679265097
sqrt(x-1)+7 = 2
>minus 2
(sqrt(x-1)+5)^2
x - 1 + 25 = 0
>simplify then minus 24
x = -24
>>679266586
>>679266389
Right, could get the thing in my head.
>>679257422
x = 26
X=26. The square root of 25 is either +5 or -5. Solution doesn't work for +5 but does for -5. Dumb niggers
>>679266586
No
(sqrt(x+1)+5)^s = (x+1)+10sqrt(x+1)+25
>>679257422
No solution. A square root can't equal a negative value.
>>679267919
Square roots can be negative. You are thinking of the square root of a negative number.
This thread is atrocious. This is only 200-level community college math, people.
>>679257422
-4 minus 1 is -5 and -5 plus 7 is positive 2. So x = 2.
i don't give a fuck just give me a prize.
>>679268413
Not everyone is a math geek, fagget.
>>679266892
This is right
>>679268413
This is literally highschool level algebra. You should learn in the 10th grade that all positive numbers have a positive and a negative square root.
>>679258394
>>679258806
Are you retarded?
1) Square roots only have both negative and positive answers if you introduce the square root into the equation
2) We are squaring something, not finding the square root of something, which ultimately negates the negative
3) if you plug in -5 for X, you get root -6 which is an imaginary number
>>679257907
Square rooting splits it in two though, this just means there is only 1 solution, some square roots give zero solutions and some give 2.
>>679264574
k
>>679270699
kek just came here to post this
>>679270699
What does (-5)^2 equal? 25 right? Same thing with (5)^2. That means the sqrt (25) can be both -5 and 5. Square roots of positive numbers have both positive and negative results. Stop being a tard
>>679270699
>>679270816
No solutions in real numbers. In complex/imaginary numbers there should be an answer, to lazy to solve it.
>>679269424
thats not true, square roots are defined as positive. You are confused with the equation
x^2 = a --> x = +-sqrt(a)
>>679257422
26. wtf this is easy
no one said x > 0, so you can use -5
>>679272439
Sauce? Cause I can pull up about 50 that say that square roots can be either positive or negative.
>>679257422
1+SQRT[5]*I or 1-SQRT[5]*I
>>679272008
okay
>>679273085
you are right they are that's why quadric equations have two solutions
>>679273258
Put a negative in front of the sqrt function. When this shit is first taught you are to see it as +/- sqrt(25) = +/- 5. Wolfram assumes it is just a positive value and solves for it as that. Kind of like what a calculator would do if you punched in sqrt (25)
>>679257422
x² + i + 7 = 2
x² + i = -5
x² = -5 -i
x = sqrt (-5 - i)
Closest thing I could come up with would be a limit.
x = lim(y->inf) 25*e^(2π-1/y)+1
>>679274031
>square root of a complex polynomial
Nigga what are you doing?
Is this supposed to be mind boggling?
Good gracious, you guys are fucking stupid.
>>679273085
sorry i got confused with real functions, only one y per x, because it wouldnt be a function otherwise
Watching people struggle with basic algebra confirms the shit hole of a society we live in.
>>679257422
(X-1)^0.5+7=2
(X-1)^0.5=-5
X-1 = i5^0.5
X=i*(5^0.5)+1
>>679274502
Shit. I meant:
x = limit (y->inf.) 25*e^(i2π-i/y)+1
X=26
X-1=25
Sqrt(25)= - 5 (-5x-5=25)
-5+7=2
>>679274920
>limits for a basic algebra problem
>>679257422
srt (x-1) + 7 = 2
srt (x-1) = -5
srt (x-1)^2 = (-5)^2
X - 1 = 25
X = 26
Suck it.
>>679275256
Bitch. The only basic thing about this problem is your sorry ass.
>>679275256
That's what happens when you start working with i, bitches.
26
>>679264457
thats literally not how i works
>>679275421
A square root of an expression cannot be negative in the reals. If X=26 then 5+7 = 2
Suck it
>>679259071
>study engineering
>still use i
Who teaches u math anon?
>>679264457
ill further elaborate
taking sqrt of a negative number gives you i
squaring i gives you a negative number and as such
sqrt(-25)=sqrt(25)i=5i
i^2=sqrt(-1)*sqrt(-1)=-1 when referencing it through exponents of (-1^1/2)*(-1^1/2) which adds exponents giving -1
so how in the fuck does sqrt(i) give you a negative value? its -1^0.25 which =/=-1
it gives you sin45+sin45i
>>679274520
>square root of a complex polynomial
https://www.google.fr/#q=square+root+of+a+complex+polynomial
>>679275822
electrical engineering uses imaginary numbers extensively
who the fuck teaches you anything?
>>679275795
OP didn't state that x>0, and all positive square roots have both a positive and negative value. 5+7 =/=2 but -5 +7 =2
Suck it
>>679257687
There's no rule against squaring a negative number, which is the opposite operation to a square root. Obligatory "you're a fucking retard"
>>679276103
positive square roots only apply when you are making the square root, it was already given and thus is only the positive half
i dont see a +/- sign anywhere
>>679259071
This. Electrical engineer reporting in, we use the letter j for sqrt(-1), since i is usually used for current. Most of the engineering fields also adopt this notation due to the extensive reach of ee in other fields.
Impossible solution. what has to be added by 7 to get 2 is -5. It is impossible to take square root and get a negative number
>>679257422
Tfw everyone who got the right answer gets called a retard
>>679276525
>It is impossible to take square root and get a negative number
That's true anon, but you can get complex numbers while taking the square root, and that's what you have to use here
>>679257422
Sqrt(x-1) + 7 = 2 [Sqr both sides]
x - 1 + 7^2 = 2^2
x - 1 + 49 = 4 [+ 1 - 49 both sides]
x = -44
----------
>>679257422
No solution. Next question
>>679276525
100% false. You can get both positive and negative values from square roots.
What people are basically saying is that (-)^2 = (+) but that sqrt (+) =/= (-) despite both of these things being the exact same shit.
>>679276742
complex numbers dont just make solutions magically work
you get a complex number from sqrt(-1) that still doesnt give you a negative solution from a sqrt
and the sqrt of the sqrt of -1 still isnt a negative number
>>679257422
x-1+7 = x+6
2 = the square root of 4, so anything under that square root must equal out to 4.
x+6 has to add up to 4, so x has to equal -4.
-4 -1 +7 = 4
so x has to be -4, right?
>>679276868
Can't do that dude. You would get
(Sqrt(x-1)+7)² =2²
>>679263853
sqrt(25i) is not -5 anon, you're getting confused there.
sqrt(25i) = sqrt(25)*sqrt(i) = 5*sqrt(i).
Now sqrt(i) = 0.707 + 0.707i, so what you wrote doesn't work out
26.
√(x - 1) + 7 = 2
√(x - 1) = -5
x - 1 = 25
x = 26
But anon is right about not continuing after -5 bc a root cannot be negative.
>>679258750
>j
Dear Engineering,
Get the fuck out of here, faggots.
Love,
Science
>>679277949
Anon. You only do that if the interior of a root is negative. Not what it equals.
http://www.mathplanet.com/education/algebra-1/exploring-real-numbers/square-roots
"All positive real numbers have two square roots, one positive and one negative."
Therefore -5 works as an answer for sqrt (25).
/thread
>>679278137
>Anon. You only do that if the interior of a root is negative. Not what it equals.
No idea what you're saying, so I'll just say it again: i^2 is -1, not sqrt(i).
sqrt(i) is actually a complex number, equal to cos(45`) + i*sin(45`)
>>679278379
>http://www.mathplanet.com/education/algebra-1/exploring-real-numbers/square-roots
Anon, you didn't read it carefully. All positive numbers have 2 square roots, but see, the square root symbol is used to denote the positive square root. so sqrt(25) = 5. If you want the other square root, you say -sqrt(25).
And like mentioned in the article, if you want to say both squareroots of a number, you write it as +/-sqrt(25).
The square root function that we use in mathematics, and the one in the OP always is the principal square root of the number inside
>>679278381
Trig doesn't really have place in this equation. i doesn't come into place unless √(-x). For instance. √(-25) = 5i. Stop over thinking.
>>679278727
Fuck. You got me. God damn troll math.
X = (-24)
>>679278787
>Trig doesn't really have place in this equation
anon, all of math is interrelated. complex numbers and trig go hand in hand.
>√(-25) = 5i
That's right, but i came into place because you mentioned it - √(25i). What made you think √i = -1? That is not true at all.
>>679279051
Nah anon, sometimes the notation in math can lead to confusion, even to mathematicians.
>>679258904
J is engineering because I is designated for current t
>>679257422
Its unpossible doofus
>>679257422
No solution.
>>679265364
>Let's see who passed intro algebra.
Were done here
>>679279584
>>679280129
x= (-24)
>>679276103
>OP didn't state that x>0,
Yes he fucking did, you must have missed the part where there wasn't a negative before the square root. Fucking autismos, I swear.
>>679280443
(7+5i) is not 2, cunt
>>679257422
What the fuck u guys are faggots!
BODMAS!!
x-1? No more like x - (1+7) since addition comes before subtraction. Fuck your guys are thick
>>679280684
X = (-24)
(-24) - 1 = (-25)
Square root of -25 = (-5)
(-5) +7 = 2
>>679257422
sqrt(x-1) + 7 = 2
sqrt(x-1) = -5
(sqrt(x-1))^2 = (-5)^2
x-1 = 25
x = 26
Is this even fap worthy?
>>679281098
fuck off faggot, don't spew nonsense.
clearly according to BODMAS, = has higher priority, so first you do 7 = 2, the answer being NO, and then sqrt(x-1) + NO which is 4pi.
>>679281171
this shit gave me cancer
>>679281098
Addition and subtraction have the same priority in order of operation. Same with multiplication and division. You process them in the order they appear.
>>679281171
>Square root of -25 = -5
no, square root of -25 = 5i, you meat calculator
>>679281171
-5*-5 is positive 25. The square root if a negative number is imaginary, generally used by the placeholder "i"
You're still correct though, because the equation becomes
i+7=2, which is the same thing as -5. But it SHOULDN'T be, because math is an asshole.
since every square root has two solutions, both the positive and the negative, this problem also has two solutions.
x = [26,no solution]
>>679281171
Is this like the scientology equivalent of math? what the actual fuck?
>>679282224
>scientology equivalent of math
kek
>>679281740
>>679281943
>>679282028
>>679282224
ok thats just how i saw it, i guess im pretty dumb
>>679257422
fuck you fuckers are fucking retarded
sqrt(x-1) + 7 = 2
sqrt(x-1) = -5
sqrt(x-1) = 5 ( i ^ 2)
[sqrt(x-1)] / [ i ] = 5 i
[sqrt(x-1)] / [sqrt (-1)] / 5 = 5 i
[sqrt(x-1)*sqrt(-1)] / [sqrt (-1) * sqrt (-1)] = 5 i
>taking the top and bottom sqrt times the sqrt of -1
[sqrt(x-1)*sqrt(-1) / -1 = 5 i
sqrt (1 - x) = - 5 i
sqrt (1-x) = -5i
you can play around with it, but ultimately, you're going to have an imaginary solution
>no real solution, but in theory, an imaginary one
>>679283160
There is no solution at all.
Not a real one.
Not an imaginary one.
NO solution.
>>679283264
>Not an imaginary one
not sure if you know what "imaginary" means
>>679283264
>>679283688
if you define alwekng as
>alwekng = -5i
then x = 1 - (alwekng)^2
>>679283264
There is only the final solution.
>>679257422
x = Kobe
>>679283819
>alwekng
what is this arbitrary mumbo jumbo
you fucking kids and your psuedo-math. You've still yet to prove there is a solution, maytee
>>679257687
cancerous faggot. the square root always has 2 solutions for real numbers: positive and negative.
>except for sqrt0
>>679284005
i mashed the keyboard, dumbass. you expect me to take the time to think of something for you?
>you still don't understand what an imaginary number is
>>679284021
You have no idea what you're talking about. Go to bed. Unless you're a yuropoor, in which case, please overdose on something.
x=78549023448
but not 100% postivie, i'm a bit drunk
.
>>679284324
but that is rounded to the nearest wole number.
rum+sleeping pille = groggyi
.
selec all of the pickup truks
>>679284249
In your 129 words and ~700 characters, you have not proven your point. At this point it's just damage control. Stop posting, nigglet.
>>67928402
Don't know if troll or just ignorant
Choosing a proper sheet for the square root, x = 1+25 e^(2\pi i) works.
It looks like most of /b/ hasn't taken elementary complex variables.
>>679283819
You call that a solution?
>>679284249
the reason i (the square root of negative 1) exists is to introduce a set of non-real numbers to satisfy the needs or theoretical equations. the number i is completely useless. just like my keyboard-mashing alwekng is useless. number i exists for no reason other than to satisfy the theoretical quantity of x^2=-1.
>theoretical quantity
>does not exist
>made up for no reason other than to satisfy a theoretical (non-existent) equation
x^2=-1 will never exist in real life. OP's equation will never exist in real life.
it's like taking a gun and turning it into a sheet of metal. The sheet of metal is useless, but it has potential to be turned back into a gun later on. Just like the number i can be multiplied by itself to give you -1 again.
>>679257422
x= -46
>>679284867
So, what's your point? It's certainly for your sake not a shoddy proof of a complex solution, I hope. Come back when you have something worth posting.
>>679284867
shut up kid
negative numbers "will never exist in real life" by your logic
>>679285011
oops, i mean x= -44
>>679258814
Depends on where in Greenland, if walking directly south. If you're in Western Greenland, it's North America, if you're in Eastern Greenland, it's either Europe or South America.
>>679285097
i mean, they don't really, when you think about. it's just a positive in an opposite direction
you can't have -1 dollars in your pocket. you can owe someone a dollar, but that negative dollar doesn't exist as a negative. only someone else's positive 1 dollar exists.
>>679284867
>will never exist in real life
Is that your argument?
Top kek, you're like a flustered child who doesn't do well in school and complains that they will never use the current subject in real life.
Deep as a puddle, anon. I expected nothing less from an aspie.
>>679285306
x^2=-1 will never represent anything in real life....
someone obviously doesn't understand theoretical math / theoretical physics
here fag.
>>679285454
>will never represent anything in real life
>theoretical
Lol, your argument is so weak, you accidentally contradicted yourself. I'm laughing so hard right now, anon.
x=1+25i
>>679285289
you have to define what you mean by "exist in real life"
numbers don't exist in real life in the sense that they aren't physical objects. They are logically consistent tools to solve problems. negative numbers and complex numbers that solve other sets of important problems.
>>679285535
(-5)^2 = 25, not (-25)
>>679285655
go finish high school, go to college, take a few math classes, and then take theoretical mathematics. then maybe you you might be less retarded
>hey look i can post a reaction image so now everyone knows i'm cool!
the whole point of imaginary mathematics is to provide solutions to imaginary problems. motion, changes in volume, etc. will never be modeled by x^2 = -1. the number i exists for no reason other than to standardize imaginary numbers. OP's equation will similarly never apply to anything in real life. there is "no real solution" but you can have an imaginary solution
>imaginary meaning you can make something up like alwekng = -5i (really, just a multiplication of the already-imaginary number i)
the whole point is that you CAN have an imaginary number. you can make up anything you want. the only issue is standardizing it.
I like feminine penis
>>679257422
sqrt(x-1)²+7²=2²
x-1+49=4
x+48=4
x=-44
>>679286068
as further education for the short-bus anon, the reason there are imaginary numbers is because there are imaginary problems. OP's equation is an imaginary problem. it's not a real equation without a real solution (which is not possible), it's an imaginary equation with an imaginary answer. every equation must have a solution; even if the equation is imaginary, it will still have a solution - just the solution will also be imaginary.
tl;dr OP's equation, which will never apply to something in real life, is imaginary and therefore has an imaginary solution
>>679286068
Who there nigger
>145 words 853 characters
fantastic damage control and projection, but I'm afraid you still were unable to prove your point.
>>679286316
>has an imaginary solution
except it doesn't.
Prove it does, anon. Humor me.
>>679286325
>tl;dr OP's equation, which will never apply to something in real life, is imaginary and therefore has an imaginary solution
that was just for you, retard
but in case even that is too complicated for your IQ of 4....
>OP equation not real
>answer not real
>hurr durrrrr
>>679286386
>not understanding what "imaginary" means
see >>679286068
>>679286185
Haha go back to school
>>679286518
>>hurr durrrrr
>ed for your IQ of 4....
nice adhom, friendo, but I still don't see an argument, or proof.
>>679286622
>all equations must have a solution
>if the equation is imaginary, the solution is imaginary
>OP's equation is imaginary
>>679286589
>Not proving your point or a solution
see pic related
>>679286729
That's not a solution.
Give me something - ANYTHING, anon. Please, I'm dyin' here.
>>679286068
sigh.
example: quantum two level systems aren't imaginary problems (idealized yes, but not imaginary, phases are real).
example 2: Neither are phase shifts in EM waves and such. At least for the EM part you can use trigonometry directly but it just gets more tedious. Analytically continuing to the complex plane makes things easier but it also allows you to model things like say, how the index of refraction of a medium can not only affect the phase of light but leads to a decay. Specifically, one deals with expressions like
E ~ exp[i n kx]
Where E is the electric field. If n has an imaginary part, you obtain decaying waves EM, which makes sense, like how cell phone signals don't penetrate into buildings, they are exponentially damped. I believe you could model both phenomena without i but it gets tedious. Yes, in the end, at least in E&M you end up with real quantities, but having i allows you to keep track of the "square roots of -1", that eventually conspire to give you real results.
>>679286622
>>679286757
>>679286833
>still not understanding imaginary numbers or their purpose
https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra
>>679257422
Quality bait
>>679286909
the wizard has spoken
>>679257422
The answer is x=5i+1 since sqrt(-1)=i, imaginary number, are you kids still in high school? Kek
>>679286970
>He continues to post nothing worthwhile, destroying valuable bandwidth and wasting valuable time in the process
>>679286970
Corollaries[edit]
Since the fundamental theorem of algebra can be seen as the statement that the field of complex numbers is algebraically closed, it follows that any theorem concerning algebraically closed fields applies to the field of complex numbers. Here are a few more consequences of the theorem, which are either about the field of real numbers or about the relationship between the field of real numbers and the field of complex numbers:
The field of complex numbers is the algebraic closure of the field of real numbers.
It looks like x is a vector of some sort, like (1+j25)
>>679257422
I just finished intro to algebra, didn't see a single thing like this.
>>679287099
>he's not smart enough to understand math above a 7th grade level
>>679287117
You're not proving anything by copying and pasting from wikipedia. Give it a break anon, it's getting sad.
>>679287117
In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.
Using Zorn's lemma, it can be shown that every field has an algebraic closure,[1][2][3] and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.
The algebraic closure of a field K can be thought of as the largest algebraic extension of K. To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K. The algebraic closure of K is also the smallest algebraically closed field containing K, because if M is any algebraically closed field containing K, then the elements of M that are algebraic over K form an algebraic closure of K.
The algebraic closure of a field K has the same cardinality as K if K is infinite, and is countably infinite if K is finite.[3]
>>679257422
26 might work.
sqrt(x-1)+7=2
sqrt(x-1)=-5
x-1=25
x=26
Now sub back in:
sqrt(26-1)+7=2
sqrt(25)=-5
sqrt(25) can be both +5 and -5 so this is technically true.
>>679287211
>Uses ad hom attacks and still to this minute fails to prove his point
>>679287279
>not being smart enough to understand what i'm copying and pasting
>because i'm not going to waste more time in an attempt to explain something to a retard
>>679287150
kek must be an ameriburger
>>679287331
>sqrt(25) can be both +5 and -5
>>679287365
>https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra
As soon as you can understand that page, you'll understand my point
>>679287476
So, no argument, then? I expected nothing less.
(x-1)^0.5 + 7 = 2
(x-1)^0.5 = -5
x-1=25
x=26
>>679287564
Why can't you just prove your point? What's so hard about that?
Linking to a different site is basically saying "look it up", which is code for "I don't know or have evidence, find it for me".
Save it anon, you're wasting everyone's time.
watching high schoolers pretend to know shit about math is fucking infuriating
>seriously not knowing what the complex plane is
wow you FUCKING idiots
>>679257422
There's no solution.
>>679257422
Fuck off anon, too lazy to do that shit right now.
>>679287476
lmao, here's your (you)
>>679287331
bait?
Your "result" is 5=-5 and that's obviouly false.
>>679287731
>Why can't you just prove your point
is basically saying "i'm not smart enough to understand your point, so there must not be one"
The fundamental theorem of algebra determines that OP's equation must have an imaginary solution to satisfy algebraic closure
as soon as you can refute that argument, i'll give your retarded ass more of my time
ayy lmao
who wants to see an actual set theoretical construction of the complex numbers from the ground up (starting with the natural numbers) using only ZFC
i'll let you pick which construction of the real numbers i should use
>>679287739
finally, someone who's not retarded
>>679287925
>must have an imaginary solution
No. It CAN'T have an imaginary solution because the value below the square root can be both positive and negative.
>implying the real numbers don't embed into the complex numbers
shaking my head
>>679259495
dunning kruger much
>>679257907
Currently in a class that's teaching exactly this. This is correct.
>>679269875
sure, if at some point in your calculations you end up with a quadratic equation. Which we didn't.
>>679257422
> Given.
√( x - 1 ) + 7 = 2
> Subtract 7 from both sides.
( √( x - 1 ) + 7 ) - 7 = ( 2 ) - 7
√( x - 1 ) = -5
> Square both sides.
( √( x - 1 ) )² = ( -5 )²
| x - 1 | = | 25 |
| x - 1 | = 25
> Break the absolute value.
x - 1 = { 25, -25 }?
> Add 1 to both sides.
( x - 1 ) + 1 = { 25, -25 }? + 1
x = { 26, -24 }?
> Check solutions for validity.
{ (x = 26 )?, ( x = -24 )? }
{ ( √( ( 26 ) - 1 ) + 7 = 2 )?, ( √( ( -24 ) - 1 ) + 7 = 2 )? }
{ ( √( 25 ) + 7 = 2 )?, ( √( -25 ) + 7 = 2 )? }
{ ( 5 + 7 = 2 )?, ( 5i + 7 = 2 )? }
{ ( 12 = 2 )?, ( 5i+7 = 2 )? }
{ False, False }
> No solutions.
>>679288211
>not knowing the difference between a square and a square root
-5 and 5, when squared, are 25
>negative 5 is, in theory, an imaginary number anyway
Proof that there is no solution:
f(x) is undefined for x<1, because any value of x that is below 1 would give an equation of complex = real and that's a false equation in any case.
Also, for any value of x above the left side is positive, while it MUST be -5, so the equation shows -5 = -5.
As simple as that, there is no solution.
>>679288714
No. See here >>679288870