Let $a,$ $b,$ $c$ be positive real numbers such that $a + b + c = 1.$  Find the minimum value of $a^2 + 2b^2 + c^2.$
Question:
Let $a,$ $b,$ $c$ be positive real numbers such that $a + b + c = 1.$  Find the minimum value of $a^2 + 2b^2 + c^2.$
Answer:
Let's think step by step.

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\frac{2}{5}
Let $a,$ $b,$ $c$ be positive real numbers such that $a + b + c = 1.$  Find the minimum value of $a^2 + 2b^2 + c^2.$
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