MathDB
Simple inequality

Source: INMO 1991 Problem 4

October 3, 2005
inequalities

Problem Statement

Let a,b,ca,b,c be real numbers with 0<a<10 < a< 1, 0<b<10 < b < 1, 0<c<10 < c < 1, and a+b+c=2a+b + c = 2. Prove that a1−a⋅b1−b⋅c1−c≥8\dfrac{a}{1-a} \cdot \dfrac{b}{1-b} \cdot \dfrac{c}{1-c} \geq 8.
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