For-all-real-values-of-x-solve-the-inequality-1-x-3-x-6-2x-3-5-1-4-

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 .

Facebook Tweet Pin