Prove the inequality.Let a, b and c be nonnegative real numbers. Let $a$, $b$ and $c$ be nonnegative real numbers. Prove that $a^4+b^4+c^2\ge 8^{½}abc$

Another way:
$$
a^4+b^4+\frac{c^2}{2}+\frac{c^2}{2}\geq 4\left(a^4b^4\frac{c^2}{2}\frac{c^2}{2}\right)^\frac 14=2^\frac 32 abc.
$$
