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I was doing some problems for Olympiad training and encountered this: How would you prove that

$(a+b+c+d)-(a+c)(b+d)\geq 1$?

We are told that $0 and the product $abcd=(1-a)(1-b)(1-c)(1-d)$.

Thanks!!

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    Tough indeed, try $a=b=c=d=1$.2011-10-30
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    Sorry restriction given is that a,b,c,d are between 0 and 1. And that $abcd=(1-a)(1-b(1-c)(1-d)$2011-10-30
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    @HenryPan Out of curiosity, from where was this taken?2011-10-30
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    Next question: interpret this probabilistically.2011-10-30
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    Me and my friend were in an advanced math class and he gave it to us. I belies it's froma book2011-10-30

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