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        riddles >> medium >> Polynomial inequality
        
(Message started by: Aryabhatta on May 22nd, 2007, 1:31pm)
Title: Polynomial inequality
Post by Aryabhatta on May 22nd, 2007, 1:31pm
If x1, x2,...,xn are positive reals whose product is 1, show that:

(a+x1)(a+x2)...(a+xn ) >= (a+1)n for any a >= 0.
Title: Re: Polynomial inequality
Post by Obob on May 27th, 2007, 4:55pm
Hint:  [hide]Try induction on n, by noticing that the n-1 numbers x_1,...,x_(n-2),x_(n-1) x_n have product 1.  [/hide]
Title: Re: Polynomial inequality
Post by Eigenray on May 27th, 2007, 7:07pm
Or you can [hide]compare the coefficient of ak on each side[/hide].


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