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Problems(1)

Inequality for 3 positive reals

Source:

10/4/2010
(YUG1)(YUG 1) Suppose that positive real numbers x1,x2,x3x_1, x_2, x_3 satisfy x1x2x3>1,x1+x2+x3<1x1+1x2+1x3x_1x_2x_3 > 1, x_1 + x_2 + x_3 <\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3} Prove that: (a)(a) None of x1,x2,x3x_1, x_2, x_3 equals 11. (b)(b) Exactly one of these numbers is less than 1.1.
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