Solve matrix equation $\|I-2x A + x^2 B\|=1$

55 Views Asked by At

Suppose $A$ and $B$ are symmetric positive definite matrices, and $x$ is a positive real number, how do I solve the following equation for $x$ and operator norm $\|\cdot\|$?

$$\|I-2x A + x^2 B\|=1$$