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Inequality on Nonnegative Reals

Source: 2018 China North Mathematical Olympiad Grade 10 Test 1 P2

July 26, 2018
inequalitiesChinathree variable inequality

Problem Statement

Let aa,bb,cc be nonnegative reals such that a2+b2+c2+ab+23ac+43bc=1a^2+b^2+c^2+ab+\frac{2}{3}ac+\frac{4}{3}bc=1 Find the maximum and minimum value of a+b+ca+b+c.
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