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Prove that (1)/(a) + (1)/(b) + (1)/(c ) ...

Prove that `(1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab)))`, where a,b,c `gt` 0

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To prove the inequality \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \geq \frac{1}{\sqrt{bc}} + \frac{1}{\sqrt{ca}} + \frac{1}{\sqrt{ab}}, \] where \( a, b, c > 0 \), we can use the Arithmetic Mean-Geometric Mean (AM-GM) inequality. ...
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