Question 100540: Please help me with this question.
Find two positive real numbers that differ by 1 and have a product of 1.
Thank you Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find two positive real numbers that differ by 1 and have a product of 1
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1st: x-y=1
2nd: xy=1
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1st: x = y+1
Substitute into 2nd to get:
(y+1)y=1
y^2+y-1=0
y = [-1 +- sqrt(1 - 4*-1)]/2
y = [-1 +- sqrt(5)]/2
Positive answer:
y = [-1+sqrt(5)]/2 = 0.618
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Substitute into 2nd to get:
x = 1/y = 0.618^-1 = 1.618
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Cheers,
stan H.
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