1. Given $x$ is a non-zero real number, and $x^{\frac{1}{2}}+x^{-\frac{1}{2}}=a$. Then $\frac{x^{2}+1}{x}=$ $\qquad$ .
$$
=1 \cdot a^{2}-2 \text {. }
$$

Let $x^{\frac{1}{2}}+x^{-\frac{1}{2}}=a$ and square both sides to get $x+x^{-1}+2=a^{2}$.
$$
\text { Then } \frac{x^{2}+1}{x}=x+x^{-1}=a^{2}-2 \text {. }
$$