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📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 The real roots of the original equation are $ u = 0, 4, 9 $. Their sum is:

📌 Question: A renewable energy system’s efficiency is modeled by the equation $ \frac{a + 2b}{a - 2b} + \frac{a - 2b}{a + 2b} = 2 $. Find $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $.

📌 Solution: Let $ x = \frac{a + 2b}{a - 2b} $. Then the equation becomes:

📌 x + \frac{1}{x} = 2

📌 Multiplying both sides by $ x $:

📌 x^2 + 1 = 2x \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1

📌 So $ \frac{a + 2b}{a - 2b} = 1 \Rightarrow a + 2b = a - 2b \Rightarrow 4b = 0 \Rightarrow b = 0 $

📌 Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this becomes:

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