Difference between revisions of "The Apple Method"

Revision as of 15:41, 21 March 2020

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

1. Evaluate: $\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$

$\emph{Solution:}$

If we set apple $=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$ , we can see that apple $^2= 6+$ apple.

@@ Line 6: / Line 6: @@
 <math>\emph{Solution:}</math>
-If we set https://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Red_apple.svg/40px-Red_apple.svg.png<math>=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that https://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Red_apple.svg/40px-Red_apple.svg.png<math>^2= 6+</math>https://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Red_apple.svg/40px-Red_apple.svg.png.
+If we set apple<math>=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that apple<math>^2= 6+</math>apple.
 Solving, we get https://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Red_apple.svg/40px-Red_apple.svg.png <math>=\boxed{3}</math>