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Home » \sum_k=0^5 (-1)^k \binom5k (5 - k)^8 - 500apps

\sum_k=0^5 (-1)^k \binom5k (5 - k)^8 - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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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}
Question: Let $ x, y, z $ be positive real numbers such that $ x + y +...
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x}.
Solution: We are to minimize the expression

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