if $(a+\sqrt{a^2+1})$ and $(b+\sqrt{b^2+1})$ are converse then prove that a and b are opposites $(a+\sqrt{a^2+1})\,(b+\sqrt{b^2+1})=1$ is supposed to equal: $b = -a$ but how do i get that? I've been trying to solve for like 2 days now.

If
$$
(a+\sqrt{a^2+1})(b+\sqrt{b^2+1})=1$$
we have
$$
a+\sqrt{a^2+1}=\sqrt{b^2+1}-b \ \ \ \ \ (1)
$$
$$
b+\sqrt{b^2+1}=\sqrt{a^2+1}-a \ \ \ \ \ (2)
$$
$(1)+(2)$ then $a=-b$.
