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Home » \[ r^2 = rac144\pi4\pi \] - Sterling Industries

\[ r^2 = rac144\pi4\pi \] - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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

📌 Substituting into the expression for $ g(u) $:

📌 g(u) = x^4 + 4x^2 + 5 = (u^2 - 4u + 4) + 4(u - 2) + 5

📌 g(u) = u^2 - 4u + 4 + 4u - 8 + 5 = u^2 + 1

📌 So, $ g(u) = u^2 + 1 $.

📌 Now substitute $ u = x^2 - 2 $:

📌 g(x^2 - 2) = (x^2 - 2)^2 + 1 = x^4 - 4x^2 + 4 + 1 = x^4 - 4x^2 + 5

📌 \boxed{x^4 - 4x^2 + 5}

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