find two numbers which are reciprocals of each other and whose sum is 5
Involving non linear equations
x + 1/x = 5
multiply each term by x
x^2 + 1 = 5x
x^2 - 5x + 1 = 0
x = (5 ± √21)/2
the two numbers are (5 + √21)/2 and 2/(5 + √21)
or
(5 - √21)/2 and 2/(5 - √21)