7. The number of real roots of the equation $8 x\left(2 x^{2}-1\right)\left(8 x^{4}-8 x^{2}+1\right)=1$ is
7. 7 detailed solutions: Let $x=\cos \theta$, then we get $8 \cos \theta \cos 2 \theta \cos 4 \theta=1$, so $\sin \theta=\sin 8 \theta \neq 0$, thus $\theta=\frac{k \pi}{8-(-1)^{k}}, k \in \mathbf{Z}$, hence $\theta=\frac{\pi}{9}, \frac{2 \pi}{7}, \frac{\pi}{3}, \frac{4 \pi}{7}, \frac{5 \pi}{9}, \frac{6 \pi}{7}, \frac{7 \pi}{9}$, a total of 7 real roots.