Suppose x_1,x_2,x_3 ∈R. Prove that one of the xi must be greater than or equal to the average (1/3)(x_(1)+x_(2)+x_(3)).

hikstac0

hikstac0

Answered question

2022-10-07

Suppose x 1 , x 2 , x 3 R . Prove that one of the x i must be greater than or equal to the average 1 3 ( x 1 + x 2 + x 3 ).

Answer & Explanation

cegukwt

cegukwt

Beginner2022-10-08Added 10 answers

Suppose not then x i < x 1 + x 2 + x 3 3 for all i { 1 , 2 , 3 }. Then summing these 3 inequalities for i = 1 , 2 , 3 we get x 1 + x 2 + x 3 < x 1 + x 2 + x 3 . Which is a contradiction.

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