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   Author  Topic: Polynomial inequality  (Read 619 times)
Aryabhatta
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Polynomial inequality  
« on: May 22nd, 2007, 1:31pm »		 Quote Quote Modify Modify
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.
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Obob
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Re: Polynomial inequality  
« Reply #1 on: May 27th, 2007, 4:55pm »		 Quote Quote Modify Modify
Hint:  Try induction on n, by noticing that the n-1 numbers x_1,...,x_(n-2),x_(n-1) x_n have product 1.  
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Eigenray
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Re: Polynomial inequality  
« Reply #2 on: May 27th, 2007, 7:07pm »		 Quote Quote Modify Modify
Or you can compare the coefficient of ak on each side.
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