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x^2+y^3>=x^3+y^4 implies x^3+y^3<=2

Source: All-Russian MO 1999

December 31, 2012
RussiaHigh school olympiadalgebraInequality

Problem Statement

Positive numbers x,yx,y satisfy x2+y3≥x3+y4x^2+y^3 \ge x^3+y^4. Prove that x3+y3≤2x^3+y^3 \le 2.
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