MathDB

6

Part of 2016 German National Olympiad

Problems(1)

Cyclic function in 7 variable with a Maximum

Source: Germany 2016 - Problem 6

6/19/2016
Let f(x1,x2,x3,x4,x5,x6,x7)=x1x2x4+x2x3x5+x3x4x6+x4x5x7+x5x6x1+x6x7x2+x7x1x3 f(x_1,x_2,x_3,x_4,x_5,x_6,x_7)=x_1x_2x_4+x_2x_3x_5+x_3x_4x_6+x_4x_5x_7+x_5x_6x_1+x_6x_7x_2+x_7x_1x_3 be defined for non-negative real numbers x1,x2,…,x7x_1,x_2,\dots,x_7 with sum 11. Prove that f(x1,x2,…,x7)f(x_1,x_2,\dots,x_7) has a maximum value and find that value.
algebracyclic functionfunctionInequalitymaximum