SOLUTION: If a, b, c are positive real numbers prove that (a + b + c)(1/a + 1/b + 1/c) >= 9 I'm lost as to how to begin this proof

Question 711123: If a, b, c are positive real numbers prove that
(a + b + c)(1/a + 1/b + 1/c) >= 9
I'm lost as to how to begin this proof
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
First you multiply and simplify.
I would also rearrange as shown below.

Next we have to show that each expression in brackets is equal or greater than 2.
All of them are of the form

We could probe it with or with .

We want to prove that

so -->
And since x and y are positive xy is a positive number we can use to divide both sides of the inequality to find that
--> -->
Then
,
and

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