Question

The value of $\sqrt{2+\sqrt{2+\sqrt{2+\dots \dots \infty }}}$ is

Answer 1

Let
$x=\sqrt{2+\sqrt{2+\dots \dots \infty }}$
$\Rightarrow x=\sqrt{2+x}\Rightarrow x^2-x-2=0$
$\Rightarrow (x+1)(x-2)=0$
$\Rightarrow x=-1,x=2$
But $x$ cannot be negative,
$\therefore x=2$