SOLUTION: I don't know what to do with this one. Please help. Here goes: Find two positive numbers that differ by 2 and have a product of 20. Match your result to the correct answer bel

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I don't know what to do with this one. Please help. Here goes: Find two positive numbers that differ by 2 and have a product of 20. Match your result to the correct answer bel      Log On


   

Question 79399: I don't know what to do with this one. Please help. Here goes:
Find two positive numbers that differ by 2 and have a product of 20. Match your result to the correct answer below:
1-sqrt21, 3-sqrt21
-1+sqrt21, -1-sqrt21
-1+sqrt21, 1+sqrt21
-1+sqrt21, -3+sqrt21
Please help. Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be A and B. From the problem description you can write:
1) A-B+=+2 and
2) A%2AB+=+20
Rewrite equation 1) as:
A+=+B%2B2 and substitute into equation 2) for A, then solve for B.
2a) %28B%2B2%29B+=+20 Simplify and subtract 20 from both sides.
B%5E2%2B2B-20+=+0 Solve this quadratic equation using the quadratic formula:
B+=+%28-2%2B-sqrt%282%5E2-4%281%29%28-20%29%29%29%2F2%281%29 Simplify.
B+=+%28-2%2B-sqrt%2884%29%29%2F2
B+=+%28-2%2B-sqrt%284%2A21%29%29%2F2
B+=+%28-2%2B-sqrt%2821%29%2A2%29%2F2
B+=+-1%2B-sqrt%2821%29
The two numbers are:
A+=+-1%2Bsqrt%2821%29
B+=+-1-sqrt%2821%29