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x + y + z = a, 1/x +1/y +1/ z = 1/a

Source: Polish MO Second Round 1962 p1

August 31, 2024
algebrasystem of equations

Problem Statement

Prove that if the numbers x x , y y , z z satisfy the equationw x+y+z=a,x + y + z = a, 1x+1y+1z=1a, \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{a}, then at least one of them is equal to a a .
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