What is the sum of the squares of all real values of x for which |2-|x| |=1?

MIRB16
Aug 20, 2017

#1**0 **

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**

Guest Aug 20, 2017