9.1

Part of 2011 All-Russian Olympiad Regional Round

Problems(1)

Problem 1 of Russian Regional Olympiad 2011, grade 9

Source:

Three positive numbers are such that the sum of any one of them with the sum of squares of the remaining two numbers is the same. Is it true that all numbers are the same? (Author: L. Emelyanov)

algebra proposedalgebra