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Home » The circumference \(C\) of the circle is given by: - Abbey Badges

The circumference \(C\) of the circle is given by: - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 \frac{2(a^2 + b^2)}{a^2 - b^2} = 3

📌 \frac{a^2 + b^2}{a^2 - b^2} = \frac{3}{2}

📌 Question: Let $ g(x^2 + 1) = x^4 + 2x^2 + 2 $. Find $ g(x^2 - 1) $.

📌 g(x^2 + 1) = x^4 + 2x^2 + 2

📌 Let’s express the right-hand side in terms of $ x^2 + 1 $.

📌 Let $ u = x^2 + 1 \Rightarrow x^2 = u - 1 $, so:

📌 x^4 = (x^2)^2 = (u - 1)^2 = u^2 - 2u + 1

📌 x^4 + 2x^2 + 2 = (u^2 - 2u + 1) + 2(u - 1) + 2

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