Let $a$ and $b$ be the roots of $x^2 - 4x + 5 = 0.$  Compute
\[a^3 + a^4 b^2 + a^2 b^4 + b^3.\]
Question:
Let $a$ and $b$ be the roots of $x^2 - 4x + 5 = 0.$  Compute
\[a^3 + a^4 b^2 + a^2 b^4 + b^3.\]
Answer:
Let's think step by step.

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Let $a$ and $b$ be the roots of $x^2 - 4x + 5 = 0.$  Compute
\[a^3 + a^4 b^2 + a^2 b^4 + b^3.\]
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