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 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 .