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\( b = 12 \) cm - Rice University

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 3Question: Let $x,$ $y,$ and $z$ be positive real numbers such that $x + y + z = 1$. Find the minimum value of $

📌 Solution: We are given that $x, y, z > 0$ and $x + y + z = 1$, and we are to minimize the expression

📌 Substituting $x + y + z = 1$, we get:

📌 For positive real numbers with fixed sum, the sum $xy + yz + zx$ is maximized when $x = y = z$. Given $x + y + z = 1$, this occurs when $x = y = z =

📌 We now verify that this is indeed the minimum. Note that for any positive $x, y, z$ with $x + y + z = 1$,

📌 Question: Let $g(x)$ be a polynomial such that

📌 Substitute $a = -2$, $b = 14$ into (1):

📌 h(4) = -2(16) + 14(4) = -32 + 56 = 24

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