36 The sum of the squares of the roots of the equation $x^{2}+|x|+1=0$ can be expressed as
A. $\sec \frac{2 \pi}{3}+\sec \frac{4 \pi}{5}$
B. $\sec \frac{3 \pi}{5}+\sec \frac{2 \pi}{3}$
C. $\sec \frac{2 \pi}{3}$
D. $\sec \frac{2 \pi}{3}+1$
36 B. It is evident that the roots of the original equation are not real. Let $x=a+bi, a, b \in \mathbf{R}$. Substituting into the equation and rearranging, we get $\left(a^{2}-b^{2}+1+\sqrt{a^{2}+b^{2}}\right)+2abi=0$. Thus, $a^{2}-b^{2}+1+\sqrt{a^{2}+b^{2}}=0$ and $2ab=0$. Solving these, the roots of the original equation are $x= \pm \frac{1+\sqrt{5}}{2} i$, and their sum of squares is $-3-\sqrt{5}$, while $\sec \frac{3 \pi}{5} + \sec \frac{2 \pi}{3}=-(3+\sqrt{5})$.