jmc

Question

Let a, b, c, d be nonnegative real numbers such that a + b + c + d = 1. Find the minimum value of a^2 + b^2 + c^2 + d^2.

Accepted Answer

By QM-AM, a^2 + b^2 + c^2 + d^24 a + b + c + d4 = 14.Then a^2 + b^2 + c^2 + d^24 116,so a^2 + b^2 + c^2 + d^2 14. Equality occurs when a = b = c = d = 14, so the minimum value is 14.