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

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Question 110078: Find two positive real numbers that differ by 1 and have a product of 1.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Find two positive real numbers that differ by 1
x, x+1
:
have a product of 1.
x(x+1) = 1
x^2 + x = 1
:
Solve this by completing the square:
x^2 + x + ___ = 1
:
x^2 + x + .25 = 1 + .25
:
(x + .5)^2 = 1.25
:
x + .5 = +/-sqrt%281.25%29
:
x = -.5 + sqrt%281.25%29 ~ +.618
and
x = -.5 - sqrt%281.25%29 ~ -1.618
:
Try them both in the original equations