SOLUTION: the sum of two numbers is 23 and their products is 132. find the two numbers.

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Question 206937: the sum of two numbers is 23 and their products is 132. find the two numbers.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be x and y, then...
1) x%2By+=+23 "the sum of two numbers is 23.."
2) x%2Ay+=+132 "...their product is 132."
Rewrite equation 1) as: x+=+23-y and substitute this for x into equation 2).
2a) %2823-y%29%2AY+=+132 Solve for y.
2a) 23y-y%5E2+=+132 Rearrange into standard quadratic form.
2a) y%5E2-23y%2B132+=+0 Factor.
2a) %28y-12%29%28y-11%29+=+0 Apply the zero product rule.
y-12+=+0 or y-11+=+0 which means that:
y+=+12 or y+=+11
The two numbers are 11 and 12.