The Apple Method

Revision as of 15:20, 21 March 2020 by Aops81619 (talk | contribs) (Examples)

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

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