Question 89
Prove that
$$
\frac{3x^2 - 2x + 3}{4} \le \sqrt[3]{\frac{x^6 + 1}{2}} \le 2x^2 - 3x + 2,
$$
for all non-negative real $x$, with equality iff $x = 1$.
$$
\frac{3x^2 - 2x + 3}{4} \le \sqrt[3]{\frac{x^6 + 1}{2}} \le 2x^2 - 3x + 2,
$$
for all non-negative real $x$, with equality iff $x = 1$.