SOLUTION: 2 positive real numbers that differ by 1 and have a product of 1

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Question 72694: 2 positive real numbers that differ by 1 and have a product of 1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2 positive real numbers that differ by 1 and have a product of 1
:
Notice they didn't say that they were integers, just real, positive numbers.
:
Let one number = x; the other number = (x+1)
:
The product = 1
x(x+1) = 1
x^2 + x = 1
x^2 + x - 1 = 0; a quadratic equation
:
Use the quadratic formula: a = 1; b = 1; c = -1
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29+
:
x+=+%28-1+%2B-+sqrt%28+1-+%28-4%29%29%29%2F%282%29+
:
x+=+%28-1+%2B-+sqrt%28+1+%2B+4+%29%29%2F%282%29+
:
x+=+%28-1+-+sqrt%28+5+%29%29%2F%282%29+
and
x+=+%28-1+%2B+sqrt%28+5+%29%29%2F%282%29+; they only want the positive number for x
:
Check using decimals: x+=+%28-1+%2B+sqrt%28+5+%29%29%2F%282%29+ = .618 rounded
.618(1.618) = .9999, close enough