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Home » #### \(12x^2 - 10x + 2\) - Silent Sales Machine

#### \(12x^2 - 10x + 2\) - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 x + \frac{1}{x} = 2 \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1.

📌 \frac{a + 2b}{a - 2b} = 1.

📌 Cross-multiplying:

📌 a + 2b = a - 2b \Rightarrow 2b = -2b \Rightarrow 4b = 0 \Rightarrow b = 0.

📌 Now substitute $ b = 0 $ into the expression we are to evaluate:

📌 \frac{a^2 + 4b^2}{a^2 - 4b^2} = \frac{a^2 + 0}{a^2 - 0} = \frac{a^2}{a^2} = 1.

📌 Question: A fish population in a polluted lake is modeled by the function

📌 where $ t $ is time in years. Find the time $ t $ at which the rate of change of the population is maximized.

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