Classical Inequalities addicts can do this. Part 4

Algebra Level 4

\[\large \frac{a^2 + b^2 + c^2 + d^2}{ab + 4bc + cd} \]

For \(a, b, c, d > 0 \), let \(\alpha \) be the minimum value of the expression above. Evaluate: \( \dfrac{(\alpha + 4)^6}{64} \) .


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