Difference between revisions of "The Apple Method"

(Why Apple?)
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==Why Apple?==
 
==Why Apple?==
A few reasons:\
+
A few reasons:
 +
 
 
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.
 
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.
 +
 
2. Apples are easier to draw.
 
2. Apples are easier to draw.
 +
 
3. Apples are good for you.
 
3. Apples are good for you.
  

Revision as of 13:27, 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.