Let n represent one such number. Then:
n - 1/n = 1 (the difference between the number n and its reciprocal is 1).
Solve for n: Multiply all three terms by n, to remove fractions:
n^2 - 1 = n, or n^2 - n - 1 = 0
Solving this for n:
-(-1) plus or minus √(1-4[1][-1])
n = ---------------------------------------------
2
1 plus or minus √5
= ----------------------------------
2
or....
x = (1+√5)/2 or x = (1-√5)/2