The Apple Method: Difference between revisions
| Line 6: | Line 6: | ||
<math>\emph{Solution:}</math> | <math>\emph{Solution:}</math> | ||
If we set <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that <math>(^{^(})^2= 6+(^{^(})</math>. | If we set <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that <math>\textcolor{red}{(\textcolor{green}{^{^(}})}^2= 6+\textcolor{red}{(\textcolor{green}{^{^(}})}</math>. | ||
Solving, we get <math>(^{^(})=\boxed{3}</math> | Solving, we get <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\boxed{3}</math> | ||
Revision as of 15:23, 21 March 2020
The Apple Method is a method for solving algebra problems. An apple is used to make a clever algebraic substitution.
Examples
1. Evaluate: ![\[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]](http://latex.artofproblemsolving.com/b/a/9/ba931c757fe2ab64fb02b7b34de5a0e22ea0b44c.png)
If we set 
, we can see that 
.
Solving, we get 
