Difference between revisions of "The Apple Method"

(Examples)
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==Examples==
 
==Examples==
 
Evaluate: <cmath>\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</cmath>
 
Evaluate: <cmath>\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</cmath>
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\emph{Solution:}
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If we set <math>apple = \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that <math>apple = \sqrt{6+\apple}</math>.
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Solving, we get <math>\boxed{apple = 3}</math>

Revision as of 09:30, 21 March 2020

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

Examples

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 $apple = \sqrt{6+\apple}$ (Error compiling LaTeX. Unknown error_msg).

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