Let $a$ and $b$ be nonzero real numbers.  Find the minimum value of
\[a^2 + b^2 + \frac{1}{a^2} + \frac{b}{a}.\]
Question:
Let $a$ and $b$ be nonzero real numbers.  Find the minimum value of
\[a^2 + b^2 + \frac{1}{a^2} + \frac{b}{a}.\]
Answer:
Let's think step by step.

user
\sqrt{3}
Let $a$ and $b$ be nonzero real numbers.  Find the minimum value of
\[a^2 + b^2 + \frac{1}{a^2} + \frac{b}{a}.\]
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