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Source: Romanian IMO TST 2006, day 3, problem 4

May 16, 2006
inequalitiescalculusalgebrathree variable inequalityromania

Problem Statement

Let a,b,ca,b,c be positive real numbers such that a+b+c=3a+b+c=3. Prove that: 1a2+1b2+1c2≥a2+b2+c2. \frac 1{a^2}+\frac 1{b^2}+\frac 1{c^2} \geq a^2+b^2+c^2.
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