Difference between revisions of "The Apple Method"

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==What is the Apple Method?==
 
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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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?==
 
==Why Apple?==
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4. An Apple a Day Keeps the Doctor Away.
 
4. An Apple a Day Keeps the Doctor Away.
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==LaTeX code for apple==
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\$(^{^(})\$
  
 
==Examples==
 
==Examples==
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==Extensions==
 
==Extensions==
 
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
 
  
 
===The pear method===
 
===The pear method===
 
When more than one variable is needed, pears, bananas, and smiley faces are usually used.
 
When more than one variable is needed, pears, bananas, and smiley faces are usually used.

Revision as of 16:25, 30 November 2020

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 $x$ 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.

4. An Apple a Day Keeps the Doctor Away.

LaTeX code for apple

$(^{^(})$

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

Extensions

The pear method

When more than one variable is needed, pears, bananas, and smiley faces are usually used.