5

Part of 2020 Korea Junior Math Olympiad

Problems(1)

max ae if a+e=1, b+c+d=3, a^2+b^2+c^2+d^2+e^2=14, a<= b<=c<=d<=e

Source: 2020 Korea Junior Math Olympiad p5 KJMO

a, b, c, d, e

be real numbers satisfying the following conditions. a \le b \le c \le d \le e, a+e=1, b+c+d=3, a^2+b^2+c^2+d^2+e^2=14Determine the maximum possible value of

ae

algebrainequalities