134. Solve the equation

$$
\left(x^{2}-a^{2}\right)^{2}=4 a x+1
$$
Solution. By adding $4 a^{2} x^{2}$ to both sides of the equation, we get:

$$
\left(x^{2}-a^{2}\right)^{2}+4 a^{2} x^{2}=4 a^{2} x^{2}+4 a x+1
$$

or

$$
\left(x^{2}+a^{2}\right)^{2}=(2 a x+1)^{2}
$$

From this: 1) $x^{2}+a^{2}=2 a x+1$, i.e., $(x-a)^{2}=1$, and therefore, $x_{1}=a+1, x_{2}=a-1$
2) $x^{2}+a^{2}=-2 a x-1$, i.e., $(x+a)^{2}=-1$. In this case, there are no solutions.

Therefore, the original equation has roots $x_{1}=a+1$ and $x_{2}=a-1$.