Difference between revisions of "The Apple Method"
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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> | ||
| + | \emph{Solution:} | ||
| + | |||
| + | If we set <math>apple = \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that <math>apple = \sqrt{6+\apple}</math>. | ||
| + | |||
| + | Solving, we get <math>\boxed{apple = 3}</math> | ||
Revision as of 08:30, 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: ![\[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]](http://latex.artofproblemsolving.com/b/a/9/ba931c757fe2ab64fb02b7b34de5a0e22ea0b44c.png)
\emph{Solution:}
If we set 
, we can see that $apple = \sqrt{6+\apple}$ (Error compiling LaTeX. Unknown error_msg).
Solving, we get 
