SOLUTION: Find two positive real numbers that differ by 2 and have a product of 10.

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Question 153153: Find two positive real numbers that differ by 2 and have a product of 10.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let one number be x, then the other one can be expressed as x + 2.
As their product is 10, we have
x(x + 2) = 10
expanding the left side, we have
x%5E2+%2B+2x+=+10
Completing square, we have
x%5E2+%2B+2x+%2B+1+=+1+%2B+10
%28x+%2B+1%29%5E2+=+11
x+=+-1%2B-+sqrt%2811%29+
So
x+=+-1%2Bsqrt%2811%29 or x+=+-1-sqrt%2811%29
So there are two solution to this problem:
(1)
one number is x+=+-1%2Bsqrt%2811%29.
The other is x%2B2+=+-1%2Bsqrt%2811%29%2B2=1%2Bsqrt%2811%29
(2)
one number is x+=+-1-sqrt%2811%29
the other is x%2B2+=+-1-sqrt%2811%29%2B2=1-sqrt%2811%29