MathNet 2022-part-04 — 197 problems (EN–VI) Question 141

Let $a$, $b$, $c$, $d$ be real numbers such that $a^4 + b^4 + c^4 + d^4 = 16$. Prove the inequality $a^5 + b^5 + c^5 + d^5 \le 32$.