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

MIRB16  Aug 20, 2017
 #1
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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

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