MathDB
Maybe old inequality with a+b+c=3

Source: Mediterranean MO 2003

October 31, 2010
inequalitiesblogsinequalities unsolvedalgebrahighschoolmathHigh school olympiad

Problem Statement

Let a,b,ca, b, c be non-negative numbers with a+b+c=3a+b+c = 3. Prove the inequality ab2+1+bc2+1+ca2+1≥32.\frac{a}{b^2+1}+\frac{b}{c^2+1}+\frac{c}{a^2+1} \geq \frac 32.
Back to ProblemsView on AoPS