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Home » Thus, the only lattice points are $(\pm 12, 0)$. - American Beagle Club

Thus, the only lattice points are $(\pm 12, 0)$. - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Factoring out $ x $:

📌 So the solutions for $ x $ are $ x = 0, 2, 3 $. Since $ x = \sqrt{u} $, we find the corresponding $ u $ values:

📌 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

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