SOLUTION: Find two positive numbers that differ by 2 and have a product of 20.

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Question 130359: Find two positive numbers that differ by 2 and have a product of 20.
Answer by solver91311(24713) About Me  (Show Source):
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One number: x
The other number: y
The difference: x - y
They differ by 2: x - y = 2
Their product is 20: x * y = 20

x-y=2, so:

x=2%2By

xy=20

%282%2By%29y=20

y%5E2%2B2y-20=0

y=%28-2%2B-sqrt%284-%284%29%281%29%28-20%29%29%29%2F2

y=%28-2%2B-sqrt%2884%29%29%2F2

y=%28-2%2B2%2Asqrt%2821%29%29%2F2 or y=%28-2-2%2Asqrt%2821%29%29%2F2

y=-1%2Bsqrt%2821%29 or y=-1-sqrt%2821%29

But y=-1-sqrt%2821%29%3C0, and the problem asked for positive numbers so exclude this root.

y=-1%2Bsqrt%2821%29

x=2%2By=2-1%2Bsqrt%2821%29=1%2Bsqrt%2821%29

Check:

1%2Bsqrt%2821%29-%28-1%2Bsqrt%2821%29%29=2

%281%2Bsqrt%2821%29%29%28-1%2Bsqrt%2821%29%29=-1%2Bsqrt%2821%29-sqrt%2821%29%2B21=20 Answer checks.