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    Hi,

    How would I go about solving this question:

    Given a, b, c are real positive such that a+b+c=1. Prove that (1+a)(1+b)(1+c) >= 8(1-a)(1-b)(1-c)
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    A BIG hint:

     x + y \geqslant 2\sqrt{xy} for all x,y > 0

     (1 + a)(1 + b)(1+c) = (2 - b - c)(2 - a - c)(2 - a - b)

    = (1 - b + 1 - c)(1 - a + 1 - c)(1 - a + 1 - b)

    Can you see how to finish up?
 
 
 
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Updated: June 19, 2017

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