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 apple $=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$ , we can see that apple $^2= 6+$ apple.

Solving, we get apple $=\boxed{3}$