Home Competitions TW-TST 2002 Problem 4
Let 0 < x 1 , x 2 , x 3 , x 4 ≤ 1 2 0<x_{1},x_{2},x_{3},x_{4}\leq\frac{1}{2} 0 < x 1 , x 2 , x 3 , x 4 ≤ 2 1 x 1 x 2 x 3 x 4 ( 1 − x 1 ) ( 1 − x 2 ) ( 1 − x 3 ) ( 1 − x 4 ) ≤ x 1 4 + x 2 4 + x 3 4 + x 4 4 ( 1 − x 1 ) 4 + ( 1 − x 2 ) 4 + ( 1 − x 3 ) 4 + ( 1 − x 4 ) 4 \frac{x_{1}x_{2}x_{3}x_{4}}{(1-x_{1})(1-x_{2})(1-x_{3})(1-x_{4})}\leq\frac{x_{1}^{4}+x_{2}^{4}+x_{3}^{4}+x_{4}^{4}}{(1-x_{1})^{4}+(1-x_{2})^{4}+(1-x_{3})^{4}+(1-x_{4})^{4}} ( 1 − x 1 ) ( 1 − x 2 ) ( 1 − x 3 ) ( 1 − x 4 ) x 1 x 2 x 3 x 4 ≤ ( 1 − x 1 ) 4 + ( 1 − x 2 ) 4 + ( 1 − x 3 ) 4 + ( 1 − x 4 ) 4 x 1 4 + x 2 4 + x 3 4 + x 4 4
Dataset text AI-MO AoPS . Quoted with source.
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