ALgebra word problem?

Question

Find two positive real numbers that difffer by 1 and have a product of 1

Answer 1

xy =1
x-y =1
y^2+y-1 = 0
y = [-1 +/- sqrt(5)]/2
y = -.5 +.5sqrt(5)
x = 1 - ( -.5 +.5sqrt(5)) = 1.5 -.5sqrt(5)

Answer 2

Form a quadratic equation.

Let the numbers be n and n+1

Then n (n+1) = 1
n^2 + n = 1
n^2 + n - 1 = 0

Use the quadratic formula and you will end with
n = -1.62 or n= 0.62 to 2 decimal places

Ans. would be -1.62 and -.62
or ans. would be .62 and 1.62