MathDB
max of \frac{(\sqrt{s_1x_1} +...+\sqrt{s_5x_5})^2}{a_1x_1+...+a_5x_5}

Source: KJMO 2012 p7

May 4, 2019
maximumpositive realSumalgebrainequalities

Problem Statement

If all xkx_k (k=1,2,3,4,5)k = 1, 2, 3, 4, 5) are positive reals, and {a1,a2,a3,a4,a5}={1,2,3,4,5}\{a_1,a_2, a_3, a_4, a_5\} = \{1, 2,3 , 4, 5\}, find the maximum of (s1x1+s2x2+s3x3+s4x4+s5x5)2a1x1+a2x2+a3x3+a4x4+a5x5\frac{(\sqrt{s_1x_1} +\sqrt{s_2x_2}+\sqrt{s_3x_3}+\sqrt{s_4x_4}+\sqrt{s_5x_5})^2}{a_1x_1 + a_2x_2 + a_3x_3 + a_4x_4 + a_5x_5} (sk=a1+a2+...+aks_k = a_1 + a_2 +... + a_k)
Back to ProblemsView on AoPS