What is the sum of the squares of all real values of $x$ for which $|2-|x| |=1$?
+128475 We can write l x l as sqrt (x^2)
So....this implies that....
sqrt [ ( (2 - sqrt (x^2) )^2 ] = 1 square both sides
( (2 - sqrt (x^2))^2 = 1 simplify
4 - 4sqrt (x^2) + x^2 = 1
x^2 + 3 = 4sqrt (x^2) square both sides again
x^4 + 6x^2 + 9 = 16x^2
x^4 - 10x^2 + 9 = 0 factor
(x^2 - 9) ( x^2 - 1) = 0
x^2 - 9 = 0 x^2 -1 = 0
x = 3 , -3 x = -1, 1 which are the values found by the guest !!!
