+753 What is the sum of the squares of all real values of x for which |2-|x| |=1?
Solve for x over the real numbers:
abs(2 - abs(x)) = 1
Split the equation into two possible cases:
2 - abs(x) = 1 or 2 - abs(x) = -1
Subtract 2 from both sides:
-abs(x) = -1 or 2 - abs(x) = -1
Multiply both sides by -1:
abs(x) = 1 or 2 - abs(x) = -1
Split the equation into two possible cases:
x = 1 or x = -1 or 2 - abs(x) = -1
Subtract 2 from both sides:
x = 1 or x = -1 or -abs(x) = -3
Multiply both sides by -1:
x = 1 or x = -1 or abs(x) = 3
Split the equation into two possible cases: x = 1 or x = -1 or x = 3 or x = -3
Sum of the squares =[1^2 + (-1)^2 + 3^2 + (-3)^2] =1 + 1 + 9 + 9 =20
