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2001 IMO Shortlist Problems/A6

Revision as of 17:17, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Prove that for all positive real numbers <math>a,b,c</math>, <center><math>\frac {a}{\sqrt {a^2 + 8bc}} + \frac {b}{\sqrt {b^2 + 8ca}} + \frac {c}{\sqrt {c^2 + 8ab}} \geq 1.<...)
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Problem

Prove that for all positive real numbers $a,b,c$,

$\frac {a}{\sqrt {a^2 + 8bc}} + \frac {b}{\sqrt {b^2 + 8ca}} + \frac {c}{\sqrt {c^2 + 8ab}} \geq 1.$

Solution

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Resources

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