For positive reals $a,b$ and $c$ with $ab+bc+ca=1$, show that
\[\sqrt{3}({\sqrt{a}+\sqrt{b}+\sqrt{c})\le \frac{a\sqrt{a}}{bc}+\frac{b\sqrt{b}}{ca}+\frac{c\sqrt{c}}{ab}.}\]
Iran TST 2012,Exam2,Day2,P4
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Re: Iran TST 2012,Exam2,Day2,P4
My solution
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