Solve the following algebraic equation: $∣ ∣ 2 x^{2} - x ∣ ∣ = 2 x^{2} - x + 8$ $|2x^2-x|=2x^2-x+8$ ?

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Answer 1 · 2016-06-20T12:33:56

$x = \frac{1}{4} (1 \pm i \sqrt{31})$ $x =1/4 (1 pm i sqrt[31])$

Making $y = 2 x^{2} - x$ $y = 2x^2-x$ we have

$| y | - y = 8$ $abs y - y = 8$

with solution $y = - 4$ $y = -4$

Now following with

$y = 2 x^{2} - x = - 4$ $y = 2x^2-x = -4$

we have the solutions

$x = \frac{1}{4} (1 \pm i \sqrt{31})$ $x =1/4 (1 pm i sqrt[31])$

Solve the following algebraic equation: ∣∣2x2−x∣∣=2x2−x+8|2x^2-x|=2x^2-x+8?