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📅 May 3, 2026 👤 scraface

May 03, 2026

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Solution: Let us define $ f(u) $ such that $ f(x^2 + 2) = x^4 + 4x^2 +...
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 $...
Solution: We are given $ p + q = 5 $ and $ pq = 6 $. We use the identi...
p^3 + q^3 = (p + q)^3 - 3pq(p + q)
p^3 + q^3 = 5^3 - 3 \cdot 6 \cdot 5 = 125 - 90 = 35

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