Prove that if $\displaystyle a,b,c>0$ then $\displaystyle \frac {ab}{a^2+3b^2}+\frac {bc}{b^2+3c^2}+\frac {ac}{c^2+3a^2}\le \frac 34$.
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Any ideas? I've tried putting $\displaystyle xyz=1$ with $\displaystyle x=\frac ab$...
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