Difference between revisions of "The Apple Method"

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The Apple Method is a method for solving algebra problems.
 
The Apple Method is a method for solving algebra problems.
 
An apple is used to make a clever algebraic substitution.
 
An apple is used to make a clever algebraic substitution.
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==Why Apple?==
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A few reasons:\
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1. When you use the Apple Method, you can box what you are substituting with the apple. When you use <math>x</math> as a substitution, instead of actually boxing it, you are just crossing it out.
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2. Apples are easier to draw.
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3. Apples are good for you.
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==Examples==
 
==Examples==
 
1. Evaluate: <cmath>\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</cmath>
 
1. Evaluate: <cmath>\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</cmath>
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===The pear method===
 
===The pear method===
 
When more than one variable is needed, pears, bananas, etc. are usually used.
 
When more than one variable is needed, pears, bananas, etc. are usually used.
===Why Apple?===
 
When you use the Apple Method, you can box what you are substituting with the apple. When you use <math>x</math> as a substitution, instead of actually boxing it, you are just crossing it out.
 

Revision as of 13:26, 17 May 2020

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

Why Apple?

A few reasons:\ 1. When you use the Apple Method, you can box what you are substituting with the apple. When you use $x$ as a substitution, instead of actually boxing it, you are just crossing it out. 2. Apples are easier to draw. 3. Apples are good for you.

Examples

1. Evaluate: \[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]

$\emph{Solution:}$

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

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

2. If \[\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdots}}} = 5\]Find x.

3. Evaluate: \[\frac{1^2+2^2+3^2+\cdots}{1^2+3^3+5^2+\cdots}\]

Extensions

The pear method

When more than one variable is needed, pears, bananas, etc. are usually used.