MathDB

E= |(x-y)/(x+y)+(x^2-y^2)/(x^2+y^2)+(x^3-y^3)/(x^3+y^3)| if x + y = 3 \sqrt{xy

Source: 2010 Moldova JBMO TST p2

February 25, 2021

algebra

Problem Statement

The positive real numbers

x

and

y

satisfy the relation

x + y = 3 \sqrt{xy}

. Find the value of the numerical expression

E=\left| \frac{x-y}{x+y}+\frac{x^2-y^2}{x^2+y^2}+\frac{x^3-y^3}{x^3+y^3}\right|.