Library / KöMaL problem A / 3 of 136
KöMaL problem A, 2014 Difficulty 5.0 AIME, harder Prove it Hungary
Prove that ( 1 + a 2 ) 2 x ( x + y ) ( 1 + b 2 ) 2 y ( x + y ) ≥ a x 2 b y 2 ( a + b 2 ) 2 x y \left(\frac{1+a}2\right)^{2x(x+y)} \left(\frac{1+b}2\right)^{2y(x+y)} \ge a^{x^2} b^{y^2} \left(\frac{a+b}2\right)^{2xy} ( 2 1 + a ) 2 x ( x + y ) ( 2 1 + b ) 2 y ( x + y ) ≥ a x 2 b y 2 ( 2 a + b ) 2 x y a , b > 0 a,b>0 a , b > 0 x x x y y y
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