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Math quiz problem
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This came up on a quiz on my phone. And i was with a friend who is better than me at math since he studies and lazy I doesnt. He tried explaining it to me.after several tries of having it explained to me i told him i got it...well i hadnt.

Problem is.i cant find the exact problem.so here is what i remember from memory ...i want to show it to a teacher and have it proper explained to me...but i need to be sure it is correct. My friend solved it and got 4...please see if it is so.so i know i can show it to another and not have it written wrong....you can also explain it...but i just want you to see if it indeed equals 4 as i have written it
>>
bump,also here it is in text form if you cant make out my letters

if x+(1/x)=2

what is the value of :

x^59 + 1/(x^59) + x^57 - 1/(x^58) +x^58 - 1/(x^57) +2
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>>33302
ι know the first part equals 2 cause duh...
and with the 2 in the ends equals 4,but i dont get how the rest equals zero
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>>33305
its more that all that junk before the 2 = x + (1/x), that is the whole problem should simplify to the first part and you'd get x + (1/x) + 2 = 4
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>>33308
sorry if im being too thick
>>
1+1/1=2
1+1+1-1+1-1+2=4
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>>33312
>>33311
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>>33312
explain it like im a 10 year old
what is 1+1/1=2? how did you get thaaaaaaat?
also why does everything equal 1
man sorry for being stupid
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>>33297

This is a simple application of the quadratic formula, or alternatively, factorization.

x + 1/x = 2
x^2 + 1 = 2x (multiply by x)
x^2 - 2x + 1 = 0 (subtract 2x from both sides)
(x-1)(x-1) = 0 (factor)
x = 1

Alternatively:
x^2 - 2x + 1 = 0
x = [2 +- sqrt(2^2 - 4*1*1)] / 2
x = [2 +- sqrt(4 - 4)] / 2
x = [2 +- 0] / 2
x = 2 / 2
x = 1

Thus:
x^59 + 1/x^59 + x^57 - 1/x^58 + x^58 - 1/x^57 + 2 =
1^59 + 1/x^59 + 1^57 - 1/1^58 + 1^58 - 1/1^57 +2 =
1 + 1 + 1 - 1 + 1 - 1 + 2 =
4
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>>33319
wow that is elementary school stuff,i feel even dumber,but i mean that requires pen an paper though doesnt it?

im wondering how my buddy figured it out in like 10 seconds,anyways more fuel for my inferiority complex fire

thanks for the concice and detailed explaination
you're the best Anon!
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>>33321

> elementary school stuff
Eh, it's not that easy. I recall this stuff surfacing around 6th and 7th grade. Sometimes freshman year of high school for certain people. Once you get a feel for it, quadratic factorization becomes intuitive mental math.

At any rate, glad I could be of help.
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>>33321
>im wondering how my buddy figured it out in like 10 seconds
Perhaps he only checked that x = 1 is a solution (1 + 1/1 = 2) and got the result 4 and only after that he checked that there are no other solutions.
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>>33297
X+1/x=2
(XX+1)=2X
XX-2X+1=0
(X-1)(x-1)=0
X=1
One to any power equals one