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User:Delmont43/Recursive equations

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Recursive equations can often be solved using the technique shown below:

Example 1

[edit]
  1. Given:
  2. Multiply both sides by 10:
  3. Subtract equation 1 from equation 2.:
  4. Simplify:

Example 2

[edit]
  1. Given:
  2. Square both sides:
  3. Simplify:
  4. Add equation 1 to equation 3.:
  5. Simplify:

Generalizing:

  1. Given:
  2. Square both sides:
  3. Simplify:
  4. Add equation 1 to equation 3.:
  5. Simplify: