Recursive equations can often be solved using the technique shown below:
Example 1
edit- Given:
- Multiply both sides by 10:
- Subtract equation 1 from equation 2.:
- Simplify:
Example 2
edit- Given:
- Square both sides:
- Simplify:
- Add equation 1 to equation 3.:
- Simplify:
Generalizing:
- Given:
- Square both sides:
- Simplify:
- Add equation 1 to equation 3.:
- Simplify: