The Apple Method

The Apple Method is a method for solving algebra problems. An apple is used to make a clever algebraic substitution.

Examples

1. Evaluate: $\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$

$\emph{Solution:}$

If we set $\textcolor{red}{(\textcolor{green}{^{^(}})}=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$ , we can see that $(^{^(})^2= 6+(^{^(})$ .

Solving, we get $(^{^(})=\boxed{3}$