6

Part of 2015 Irish Math Olympiad

Problems(1)

x,y>0 and x + y <= 1 prove 8xy <= 5x(1 - x) + 5y(1 - y)

Source: Irmo 2015 p2 q6

x,y

are nonnegative real numbers such that

x + y \le 1

8xy \le 5x(1 - x) + 5y(1 - y)

and determine the cases of equality.

algebrainequalitiesalgebraic inequality