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

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Question 4188: Find two positive real numbers that differ by 1 and have a product of 1.

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let first number be x. Therefore second number must be x+1.

Their product is 1 --> x(x+1) = 1

so we get x%5E2+%2B+x+-+1+=+0

Put this into the quadratic formula, since it does not factorise easily and you get x=%28-1%2Bsqrt%285%29%29%2F2 or x=%28-1-sqrt%285%29%29%2F2

Since the question says the numbers are positive, then the answer is x=%28-1%2Bsqrt%285%29%29%2F2.

Working this out, gives x=0.618

CHECK: 0.618*1.618 = 0.999924, which is close enough, since we rounded the actual answer to 3 decimal places.

jon.