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Home » You Won’t Believe What Xemu Does in Just 60 Seconds! 🔥 - Coaching Toolbox

You Won’t Believe What Xemu Does in Just 60 Seconds! 🔥 - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 5Question: Let $ f(x) $ be a polynomial such that $ f(x^2 + 2) = x^4 + 4x^2 + 4 $. Find $ f(x^2 - 2) $.

📌 Solution: Let us define $ f(u) $ such that $ f(x^2 + 2) = x^4 + 4x^2 + 4 $. Observe that the right-hand side can be rewritten as:

📌 x^4 + 4x^2 + 4 = (x^2 + 2)^2

📌 Thus, $ f(x^2 + 2) = (x^2 + 2)^2 $, which implies that $ f(u) = u^2 $.

📌 Now, substitute $ u = x^2 - 2 $ into $ f(u) $:

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

📌 oxed{x^4 - 4x^2 + 4}

📌 Question: Let $ p $ and $ q $ be real numbers such that $ p + q = 5 $ and $ pq = 6 $. Find the value of $ p^3 + q^3 $.

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