What is the answer to |x|^2-|x|+4=2x^2-3|x|+1 ?

The answer to |x|^2-|x|+4=2x^2-3|x|+1 is x=-3\lor x=3

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|x|^2-|x|+4=2x^2-3|x|+1

∣ x ∣^{2} - ∣ x ∣ + 4 = 2 x^{2} - 3 ∣ x ∣ + 1

x = - 3 or x = 3

Solution steps

∣ x ∣^{2} - ∣ x ∣ + 4 = 2 x^{2} - 3 ∣ x ∣ + 1

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x = - 3 or x = 3

∣ x ∣ + 2 ∣ x - 1 ∣ - 3 ∣ x - 2 ∣ = 4

11 + 5 ∣ x - 1 ∣ = 17

∣ x - 3 ∣ + ∣ x + 2 ∣ - ∣ x - 4 ∣ = 3

∣ x - 1 ∣ + ∣ x - 2 ∣ = 2

∣ x ∣ + 2 ∣ x - 6 ∣ = 12

What is the answer to |x|^2-|x|+4=2x^2-3|x|+1 ?
The answer to |x|^2-|x|+4=2x^2-3|x|+1 is x=-3\lor x=3
Solve for x: |x|^2-|x|+4=2x^2-3|x|+1
The solution is x=-3\lor x=3