368*. Solve the equation:

$$
x^{2}+\frac{x^{2}}{(x+1)^{2}}=1
$$
$\triangle$ Subtract $\frac{2 x^{2}}{x^{2}+1}$ from both sides of the equation to obtain a square of a difference on the left side:

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

Now, the obvious substitution $-\frac{x^{2}}{x+1}=y$. Complete the solution on your own.

Answer: $(\sqrt{2}-1 \pm \sqrt{2 \sqrt{2}-1}) / 2$.