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2023 WSMO Speed Round Problems/Problem 7

Problem

Let $e, a, j$ be real numbers such that $e + a + j = 1$ and $e\geq -\frac{1}{3}$, $a\geq 1$ and $j\geq-\frac{5}{3}$. Find the maximum value of $\sqrt{3e+1} + \sqrt{3a+3} + \sqrt{3j+5}.$

Solution

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