Question 98
Find all real numbers $x,y$ such that
$$\left(x-\sqrt{x^2+1}\right)\left(y-\sqrt{y^2+1}\right)=1\quad\text{and}\quad(x^2+y+2)(y^2+x+2)=8.$$
$$\left(x-\sqrt{x^2+1}\right)\left(y-\sqrt{y^2+1}\right)=1\quad\text{and}\quad(x^2+y+2)(y^2+x+2)=8.$$