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Composite Function

If |6x2 - ...

Question

If $| 6 x^{2} - 5 x - 1 | = 5 x - 6 x^{2} - 1,$ then determine x.

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Solution

$6 x^{2} - 5 x - 1 = (x - 1) (6 x + 1)$
$∴ x = - 1 / 6, 1$
Consider two cases :
(I) $x < - \frac{1}{6}, o r x > 1, L . H . S = + i v e$
(II) $- \frac{1}{6} \leq x \leq 1, L . H . S . = - i v e$
Ans. $\frac{1}{2} (- 1 \pm \sqrt{5}) .$

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