For all real values of x solve the inequality ∣((1−x^3 )/(x^6 −2x^3 +5))∣≤(1/4)


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Question Number 41095 by Necxx last updated on 02/Aug/18

$F o r a l l r e a l v a l u e s o f x s o l v e t h e$ $i n e q u a l i t y$ $∣ \frac{1 - x^{3}}{x^{6} - 2 x^{3} + 5} ∣⩽ \frac{1}{4}$
	Answered by ajfour last updated on 02/Aug/18

	$l e t x^{3} - 1 = t$ $\Rightarrow ∣ \frac{t}{t^{2} + 4} ∣⩽ \frac{1}{4}$ $o r - \frac{1}{4} ⩽ \frac{t}{t^{2} + 4} ⩽ \frac{1}{4}$ $o r t^{2} + 4 t + 4 ⩾ 0 a n d$ $t^{2} - 4 t + 4 ⩾ 0$ $\Rightarrow t \in (- \infty, \infty)$ $t h e s a m e f o r x .$
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