What is the answer to |x|(|x|-2)=3 ?

The answer to |x|(|x|-2)=3 is x=-3\lor x=3

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|x|(|x|-2)=3

∣ x ∣ (∣ x ∣ - 2) = 3

x = - 3 or x = 3

Solution steps

∣ x ∣ (∣ x ∣ - 2) = 3

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x = - 3 or x = 3

∣ 3 x - 2 ∣ + 1 = - 1

∣ x + 1 ∣ = - ∣ 2 x - 3 ∣

x^{3} - 2 x^{2} + x = 2

(x - 2)^{2} - 3 ∣ x - 2 ∣ + 2 = 0

∣ x ∣ + ∣ x - 2 ∣ + ∣ x - 4 ∣ = 5