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

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: Find two positive real numbers that differ by 1 and have a product of 1.      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 122302: Find two positive real numbers that differ by 1 and have a product of 1.
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the first number A.
Let's call the second number B.
1.B=A-1 Differ by 1.
2.AB=1 Product equals 1.
Use B as a function of A of equation 1 in equation 2.
AB=1
A%28A-1%29=1
A%5E2-A=1
A%5E2-A-1=0
Using the quadratic formula,
A+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A%281%29%2A%28-1%29+%29%29%2F%282%29+
A+=+%281+%2B-+sqrt%281%2B4+%29%29%2F%282%29+
A+=+%281+%2B-+sqrt%285%29%29%2F%282%29+
A%5B1%5D=+%281+%2B+sqrt%285%29%29%2F%282%29+
A%5B2%5D=+%281+-+sqrt%285%29%29%2F%282%29+
Since A%5B2%5D%3C0, we only have one solution.
highlight%28A=+%281+%2B+sqrt%285%29%29%2F%282%29+%29
B=A-1
highlight%28B=%28sqrt%285%29%29%2F%282%29%29+
Approximately,
A=1.618
B=0.618