Find all solutions of the equation $(| x | + 1)^{2} = 4 | x | + 9$ belonging to the domain of definition of the function $y = \sqrt{5 - 2 x}$

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Solution

$5 - 2 x \geq 0$
$2 x - 5 \leq 0$
$x \in (- \infty, \frac{5}{2})$
Let $| x | = t$ , $t \geq 0$
$(t + 1)^{2} = 4 t + 9$
$t^{2} + 2 t + 1 = 4 t + 9$
$t^{2} - 2 t - 8 = 0$
$(t - 4) (t + 2) = 0$
$∴ t = 4 o r - 2$
$t = 4$
$| x | = 4$
$x = \pm 4$
$∴ x = - 4$

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