Question

How would you prove the statement: sqrt(5) / 5 ((1+sqrt(5))/2) - sqrt(5)/5 ((1-sqrt(5))/2) by strong induction ?

Answer 1

We cannot see any statement in your question. The formula you wrote equals 1. It will look like the formula for n-th term of Fibonacci sequence, if you rise both (1+sqrt(5))/2 and (1-sqrt(5))/2 to the power n.