x^2 - 2x + 5 = 0
Let the roots be m and n
The sum of the roots = 2
So m + n = 2
And the product of the roots = mn = 5
Call the reciprocals of the roots 1/m = a , 1/n = b... and their sum = 1/m + 1/n = a + b ...simplify as
(m+ n) 2
______ = _____ = sum of the reciprocals
mn 5