Question

How is this possible?

Answer 1

I never knew that\[(x-2)^2=(2-x)^2\]

Answer 2

idk

Answer 3

\[\huge\rm (2-x)^2\] is same as \[[ -(-2+x)^2]^2\]

Answer 4

hihihi... expand both sides???

Answer 5

Because the absolute value of |a-b| = |b-x|

Answer 6

opps typo

Answer 7

And raising them to the power of 2 makes them both positive.

Answer 8

\(x^2-4x+4=4-4x+x^2\)

Answer 9

\[[ -(-2+x)]^2\] ***
which is same as \[[ - (x-2)]^2\]
and we know (negative) to the even power is always positive

Answer 10

How can they be not equal??

Answer 11

I don't know, I never realized that those were equal. I wish I could give more than 1 medal, but thanks for the help!

Answer 12

Actually, if \(A^2=B^2\), then \(\pm A =\pm B\)

Answer 13

Hence, you have 4 cases
A = B
A = -B
-A = B
-A = -B
If A = B , then x-2 = 2 -x, that gives us x = 2 , So. when x = 2 , (x-2)^2 (2-x)^2

If A = -B , sure, for all x