SOLUTION: The product of two numbers is 323 and the difference between them is 2. What are the two numbers?

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Question 1105160: The product of two numbers is 323 and the difference between them is 2. What are the two numbers?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
x*(x-2) = 323.


Solve this quadratic equation.


Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Since the numbers differ by only 2, they are nearly the same number; so just look for a perfect square that is close to 323.

18%5E2+=+324; and you know from basic algebra that %28x%2B1%29%28x-1%29+=+x%5E2-1. So %2818%2B1%29%2818-1%29+=+18%5E2-1+=+324-1+=+323.

The two numbers are 17 and 19.

Then you have to remember that the two numbers could both be negative, so another answer is -17 and -19.

Or, if you want to solve the problem algebraically, call the numbers x-1 and x+1 instead of x and x+2 or x and x-2. Then the algebra is a lot easier, because you don't have to factor a quadratic equation:

%28x-1%29%28x%2B1%29+=+x%5E2-1+=+323
x%5E2+=+324
x+=+18 or x+=+-18

The two numbers are x-1=17 and x+1=19, or x-1=-19 and x+1=-17.