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$\begingroup$

How to show that

$$ \displaystyle (a_1 + a_2 + a_3)(\frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3}) \ge 9 $$

$a_1,a_2,a_3$ are all of same algebraic sign.

  • 1
    Is this for a class? If so, what class?2010-12-04
  • 0
    It's valid only when the numbers $a_1,a_2,a_3$ are all positive or all negative. A simple counter example would be $2,-1000,2$. I shall edit it.2013-03-23

6 Answers 6