SOLUTION: Quadratic equations: Find two possitive numbers that differ by 2 and have a producy of 20. The answer is -1 + squareroot of 21 and 1 + squareroot of 21. How do I at the a

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Quadratic equations: Find two possitive numbers that differ by 2 and have a producy of 20. The answer is -1 + squareroot of 21 and 1 + squareroot of 21. How do I at the a      Log On


   

Question 4306: Quadratic equations:
Find two possitive numbers that differ by 2 and have a producy of 20.
The answer is -1 + squareroot of 21 and 1 + squareroot of 21.
How do I at the answer. (need steps)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, assign the variables:
Let the two numbers be x and y
Then: x - y = 2 Rewrite as: x = y + 2 and substitute into the 2nd equation.
and xy = 20
(y+2)y = 20
y^2 + 2y = 20
y^2 + 2y - 20 = 0 Solve by use of the quadratic formula:
y=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
y=%28-2%2B-sqrt%28-2%5E2-4%2A1%2A%28-20%29%29%29%2F%282%2A1%29
y=%28-2%2B-sqrt%284%2B80%29%29%2F%282%29
y=%28-2%2B-sqrt%284%2A21%29%29%2F%282%29
y=%28-2%2B-2sqrt%2821%29%29%2F%282%29
y=-1%2B-sqrt%2821%29
x = y + 2
x=2%2B%28-1%2B-sqrt%2821%29%29
x=1%2B-sqrt%2821%29