Problem

Source: 2015 Taiwan TST Round 1 Quiz 3 Problem 1

Tags: inequalities, Taiwan, algebra, Taiwan TST 2015



Let $a,b,c,d$ be any real numbers such that $a+b+c+d=0$, prove that \[1296(a^7+b^7+c^7+d^7)^2\le637(a^2+b^2+c^2+d^2)^7\]