SAT: Math question regarding quadratic equations?

Question

If x + 1/x = 2, what is the value of x^2 + 1/x^2 ?

When possible, with explanation please.
Thanks in advance!

Answer 1

x+1/x =2
(x^2+1)/x=2
x^2+1=2x [By cross-multiplication]
x^2-2x+1=0
(x-1)^2=0
x=1
Therefore,x^2+1/x^2
=(1)^2+1/1^2
=1+1=2

Answer 2

X+1/X=2

SO x=2

4+1/4= 5/4 =1.25

Answer 3

First, find solution for first equation:

x + 1/x = 2
x^2 + 1 = 2x
x^2 - 2x + 1 = 0 --> this is your quadratic equation, then:
(x -1)^2 = 0
Then : x - 1 = 0
x = 1

Use this answer to second equation:

x^2 + 1/x^2
1^2 + 1/1 ^2
1 + 1 = 2

And that's your value....Ciao

Answer 4

x + 1/x = 2

multiply x for both sides
x^2 + 1 = 2x

subtract 2x for both sides
x^2 - 2x + 1 = 0

factor
(x - 1) (x - 1) = 0

(x - 1)^2 = 0

take a square root
x - 1 = 0

add 1 for both sides
x = 1

so 1^2 + 1/1^2 = 1 + 1 = 2 <== answer

Answer 5

x + 1/x = 2
x² + 1 = 2x
x² - 2x + 1 = 0
(x - 1)² = 0
x = 1
_______

x² + 1/x² = 1² + 1/1² = 1 + 1 = 2

Answer 6

(1) + 1(1) = 2, so (1)^2 + 1/(1)^2 also equals 2!