Difference between revisions of "The Apple Method"
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Solving, we get <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\boxed{3}</math> | Solving, we get <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\boxed{3}</math> | ||
− | 2. If <cmath>\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdots}}} = 5</cmath>Find x. | + | 2. If <cmath>\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdots}}} = 5</cmath> |
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+ | Find x. | ||
+ | |||
+ | <math>\emph{Solution:}</math> | ||
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+ | If we set <math>\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdots}}}</math> equal to <math>\textcolor{red}{(\textcolor{green}{^{^(}})},</math> we get <math>\textcolor{red}{(\textcolor{green}{^{^(}})} = 5</math> and <math>\textcolor{red}{(\textcolor{green}{^{^(}})}^2 = x \cdot \textcolor{red}{(\textcolor{green}{^{^(}})} = 25.</math> | ||
+ | |||
+ | Simplifying, we find <math>\textcolor{red}{(\textcolor{green}{^{^(}})} = x,</math> so <math>x = 5.</math> | ||
3. Evaluate: <cmath>\frac{1^2+2^2+3^2+\cdots}{1^2+3^2+5^2+\cdots}</cmath> | 3. Evaluate: <cmath>\frac{1^2+2^2+3^2+\cdots}{1^2+3^2+5^2+\cdots}</cmath> |
Revision as of 00:37, 20 February 2021
Contents
[hide]What is the Apple Method?
The Apple Method is a method for solving algebra problems. An apple is used to make a clever algebraic substitution.
Dr. Ali Gurel from Alphastar academy started a new series of cool videos; the apple method's corresponding video can be found at https://www.youtube.com/watch?v=rz86M2hlOGk
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.
4. An Apple a Day Keeps the Doctor Away.
LaTeX code for apple
$(^{^(})$
Examples
1. Evaluate:
If we set , we can see that .
Solving, we get
2. If
Find x.
If we set equal to we get and
Simplifying, we find so
3. Evaluate:
Extensions
The pear method
When more than one variable is needed, pears, bananas, and smiley faces are usually used.