Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "The Apple Method"

(→‎Examples)
(→‎Examples)
Line 6: Line 6:
 
<math>\emph{Solution:}</math>
 
<math>\emph{Solution:}</math>
  
−
If we set apple<math>=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that apple<math>^2= 6+</math>apple.
+
If we set <math>(^{^(})=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}</math>, we can see that <math>(^{^(})^2= 6+(^{^(})</math>.
  
−
Solving, we get apple <math>=\boxed{3}</math>
+
Solving, we get <math>(^{^(})=\boxed{3}</math>

Revision as of 16:20, 21 March 2020

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

Examples

1. Evaluate: \[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]

$\emph{Solution:}$

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

Solving, we get $(^{^(})=\boxed{3}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=The_Apple_Method&oldid=119906"