12. Let $a, b$ be real numbers, and the equation $x^{4}+a x^{3}+b x^{2}+a x+1=0$ has at least one real root. Find the minimum value of $a^{2}+b^{2}$.
12. Make the substitution $y=x+\frac{1}{x}$, transforming it into $y^{2}+a y+(b-2)=0$ which has at least one real root with an absolute value greater than or equal to 2, and find that $\left(a^{2}+b^{2}\right)_{\min }=\frac{4}{5}$.