How do you solve x^3 -|x|=0?

1 Answer
MattyMatty
Feb 11, 2018

x = 0 or 1

Explanation:

"Apply the definition of |x| : "
= {( x ", " x >= 0), (-x", " x<=0) :}

"Now take first the case "x >= 0 " : "
"Then we have"
x^3 - x = 0
=> x(x^2 - 1) = 0
=> x(x-1)(x+1) = 0
=> x = cancel(-1), 0, or 1
"We eliminate x= -1 as we made the assumption "x>=0"."

"Then take the second case "x <= 0" : "
"Then we have"
x^3 + x = 0
=> x(x^2 + 1) = 0
=> x = 0 " (x² + 1 > 0 and has no real solutions)"

"So we have only x=0, or 1 as real solution of the equation."

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