How to solve the following equation:
$x \arcsin(x^2) + 2\sqrt{1-x^2}\arcsin(x) = 2x $
I think it is hard. Thanks.
How to solve the following equation:
$x \arcsin(x^2) + 2\sqrt{1-x^2}\arcsin(x) = 2x $
I think it is hard. Thanks.
There are only three roots, in $\{-u,0,u\}$, with $u$ pretty close to $1$. By convexity, the Newton method with starting point $x_0=\pm 1$ has quadratic convergence.