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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 $=\boxed{3}$

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