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Part of 1983 Austrian-Polish Competition

Problems(1)

a^5 + b^5 <= 1 and x^5 + y^5 <= 1 then a^2x^3 + b^2y^3 <= 1 for a,b,x,y>=0

Source: Austrian Polish 1983 APMC

4/30/2020
Nonnegative real numbers a,b,x,ya, b,x,y satisfy a5+b5≤a^5 + b^5 \le 1 and x5+y5≤1x^5 + y^5 \le 1. Prove that a2x3+b2y3≤1a^2x^3 + b^2y^3 \le 1.
inequalitiesalgebra