Problem

Source: Polish MO Second round 2024 P5

Tags: inequalities



The positive reals $a, b, c, x, y, z$ satisfy $$5a+4b+3c=5x+4y+3z.$$Show that $$\frac{a^5}{x^4}+\frac{b^4}{y^3}+\frac{c^3}{z^2} \geq x+y+z.$$ Proposed by Dominik Burek