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$x^3 + y^4\leq x^2 + y^3$

Source: 13-th Hungary-Israel Binational Mathematical Competition 2002

April 7, 2007

inequalities proposedinequalitiesalgebra

Problem Statement

Suppose that positive numbers

x

and

y

satisfy

x^{3}+y^{4}\leq x^{2}+y^{3}

. Prove that

x^{3}+y^{3}\leq 2.