SOLUTION: Checking my math on this one, we're working on Quadratics this week: Find two positive real numbers that differ by 1 and have a product of 1

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!