inequality

How I prove this inequality :(a+b+c)(1/a+1/b+1/c)=>9?:(

Write the second factor as \(\displaystyle \dfrac{bc+ac+ab}{abc}\). The carefully multiply the two factors.

This is a fact: \(\displaystyle \forall (x~\&~y)[x^2+y^2\ge 2xy]\). You will use that three times.
 
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