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Nice Inequality with Partial Sums of Squares

Source: Hungary-Israel Mathematical Competition 2007 Problem 2

November 19, 2007
inequalitiesinequalities unsolvedalgebra

Problem Statement

Let a,b,c,d a,b,c,d be real numbers, such that a^2\le 1, a^2 \plus{} b^2\le 5, a^2 \plus{} b^2 \plus{} c^2\le 14, a^2 \plus{} b^2 \plus{} c^2 \plus{} d^2\le 30. Prove that a \plus{} b \plus{} c \plus{} d\le 10.
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