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prove that for any three real distinct numbers, a , b and c when a+b+c = 1
(1+a)(1+b)(1+c) > 8(1-a)
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Rewrite the problem by substituting 1 by (a+b+c) as having to prove that
Setting
given x+y+z=1, to prove that
Multiplying the above three inequalities concludes the solution |
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and dividing by each factor on both sides by 2, we can further rewrite as
which is well known and easy as
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