MathDB

1

Part of 2001 Greece Junior Math Olympiad

Problems(1)

Inequality

Source: Archimedes 2001 Junior

3/17/2020
Let a,b,x,ya, b, x, y be positive real numbers such that a+b=1a+b=1. Prove that 1ax+by≤ax+by\frac{1}{\frac{a}{x}+\frac{b}{y}}\leq ax+by and find when equality holds.
inequalities