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

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

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|x-3|=x^2-3

∣ x - 3 ∣ = x^{2} - 3

x = - 3 or x = 2

Solution steps

∣ x - 3 ∣ = x^{2} - 3

Find positive and negative intervals

x < 3, x \geq 3

Solve the inequality for each interval

(x = - 3 or x = 2) or No Solution

x = - 3 or x = 2

(5^{2}) (5^{4})

5 - 3 (2 x - 7) > 12 - 5 (x - 2)

10 = \frac{x}{10}

(x - \frac{3}{2}) (2 x - \frac{9}{2}) = 11

∣ 2 a - 1 ∣ < 3