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?== | ||
| + | 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. | ||
| + | 2. Apples are easier to draw. | ||
| + | 3. Apples are good for you. | ||
| + | |||
==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. | ||
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Revision as of 14:26, 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 
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: ![\[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]](http://latex.artofproblemsolving.com/b/a/9/ba931c757fe2ab64fb02b7b34de5a0e22ea0b44c.png)
If we set 
, we can see that 
.
Solving, we get 
2. If ![\[\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdots}}} = 5\]](http://latex.artofproblemsolving.com/5/5/0/5500be6aeb9adf10d0b25bcdcbeea78f7b9c7098.png)
Find x.
3. Evaluate: ![\[\frac{1^2+2^2+3^2+\cdots}{1^2+3^3+5^2+\cdots}\]](http://latex.artofproblemsolving.com/5/1/e/51ebeab998a84de66e0d06d6d48891f9b18f1820.png)
Extensions
The pear method
When more than one variable is needed, pears, bananas, etc. are usually used.
