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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

November 24, 2021
algebrainequalities

Problem Statement

Let a,b,c,d,ea, 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 aeae.