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Difference between revisions of "The Apple Method"

(→‎Examples)
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<math>\emph{Solution:}</math>
 
<math>\emph{Solution:}</math>
  
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If we set apple<math>=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that apple<math>^2= 6+</math>apple.
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If we set <math>(^{^(})=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that <math>(^{^(})^2= 6+(^{^(})</math>.
  
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Solving, we get apple <math>=\boxed{3}</math>
+
Solving, we get <math>(^{^(})=\boxed{3}</math>

Revision as of 15:20, 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: \[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]

$\emph{Solution:}$

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

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

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