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If $x,y,z>0.$ Then prove that $\displaystyle \frac{yz}{x}+\frac{zx}{y}+\frac{xy}{z}\geq x+y+z$

what i try

put $\displaystyle x=a/b,y=b/c,z=c/a$ and $xyz=1$

Then $\displaystyle \frac{b^2}{a^2}+\frac{c^2}{b^2}+\frac{a^2}{c^2}\geq \frac{(a+b+c)^2}{a^2+b^2+c^2}$ (Titu,s lima)

How do i solve it Help me please

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marked as duplicate by Martin R, Community Mar 27 at 19:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Hint : $ yz/x + xz/y \ge 2z$

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It's $$\sum_{cyc}(x^2y^2-x^2yz)\geq0$$ or $$\sum_{cyc}z^2(x-y)^2\geq0.$$

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