SOLUTION: Find two positive real numbers that differ by 1 and have a product of 1.

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Question 48610:
Find two positive real numbers that differ by 1 and have a product of 1.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be x and y
EQUATIONS:
1st: x-y=1
2nd: xy=1

x=y+1
(y+1)(y)=1
y^2+y-1=0
Use the quadratic formula to get:
y=[-1+-sqrt(1+4)]/2
y=(-1/2)+-(1/2)sqrt5
Substitute to solve for "x", as follows:
x-[(-1/2)+-(1/2)sqrt5]=1
x=1+(-1/2)+-(1/2)sqrt5
x=(1/2)+-(1/2)sqrt5
Cheers,
Stan H.