SOLUTION: if a,b,c,d > 0 and abcd=1, prove that (1+a)(1+b)(1+c)(1+d) >= 2^4

SOLUTION: if a,b,c,d > 0 and abcd=1, prove that (1+a)(1+b)(1+c)(1+d) >= 2^4

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Question 461595: if a,b,c,d > 0 and abcd=1, prove that (1+a)(1+b)(1+c)(1+d) >= 2^4
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
First up, let S = (1+a)(1 + b)(1 + c)(1 + d) = 1+c + d + cd + b + bc + bd + bcd + a + ac + ad + acd + ab + abc + abd + abcd. (This expression has 16 terms.)
By the AM-GM inequality, we have
, since abcd = 1.
Hence
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