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Home » = \sqrt{ \frac3a2 \cdot \left(\fraca2 + 1\right) \cdot \left(\fraca{ - AMAZONAWS

= \sqrt{ \frac3a2 \cdot \left(\fraca2 + 1\right) \cdot \left(\fraca{ - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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F(2) = \frac{100 \cdot 2}{2^2 + 4} = \frac{200}{8} = 25.
Question: A meteorologist studying rainfall patterns defines a functio...
Solution: We analyze the cubic polynomial $ R(x) = x^3 - 3x + 2 $. To...
R(1) = 1 - 3 + 2 = 0 \Rightarrow x = 1 \text{ is a root}.
Divide $ R(x) $ by $ x - 1 $ using synthetic division:
\begin{array}{r|rrrr}
& 1 & 0 & -3 & 2 \\
& & 1 & 1 & -2 \\
& 1 & 1 & -2 & 0 \\
So $ R(x) = (x - 1)(x^2 + x - 2) $. Factor the quadratic:

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abc = rac{x}{y} \cdot rac{y}{z} \cdot rac{z}{x} = 1.
We are to minimize
a + b + c - \log\left(rac{x}{z} + rac{z}{x}
ight) = a + b + c - \log\left(rac{1}{b} + b
since $ rac{x}{z} = rac{x}{y} \cdot rac{y}{z} = ac = rac{1}{b} $,...
a + b + c - \log\left(b + rac{1}{b}
Since $ abc = 1 $, we can assume $ a = rac{x}{y} $, $ b = rac{y}{z}...
a + b + c \geq 3\sqrt[3]{abc} = 3.
Equality occurs when $ a = b = c = 1 $, i.e., when $ x = y = z $.
Now consider the second term:

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