Find two positive real numbers that differ by 1 and have a product of 1 Let one of the real number be x and the other be y. Both differ by 1: y-x = 1 Both have a product of 1 : xy = 1 We have a pair of simultaneous equations y-x = 1....(1) xy = 1....(2) Manipulate (1): y-x = 1 y = (x+1)....(3) Substitute (3) into (2): xy = 1 x(x+1) = 1 x^2 + x = 1 x^2 + x -1 = 0 ---- Oooo...a quadratic equation! I'm not going to bother factorising it as I remember the answer to this equation. It gives a golden ratio as its' answer -- something like 0.618. So if x = something like 0.618 Then y = x + 1 = something like 1.618 Hope that helps!