Find all real solutions of the equation $x^{2}+2 x \sin (x y)+1=0$.

#
Consider the given equation as a quadratic equation in terms of $x$. Its discriminant is equal to 4 ( $\sin ^{2}(x y)-$ 1). The discriminant must be non-negative, so $\sin (x y)= \pm 1$. From this, $|x|=1, \sin y=-1$.

## Otvet

$x= \pm 1, y=-\pi / 2+2 k \pi$