SOLUTION: the product of two consecutive integers is 143. find their sum

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Question 954937: the product of two consecutive integers is 143. find their sum
Answer by macston(5194) About Me  (Show Source):
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There is no solution for consecutive integers (the product of an odd and even number is always even), but solution using consecutive odd integers follows.The product of two consecutive odd integers is 143. find their sum
x=first integer; x+2=second integer
x(x+2)=143
x%5E2%2B2x-143=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-143+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-143=576.

Discriminant d=576 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+576+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+11
x%5B2%5D+=+%28-%282%29-sqrt%28+576+%29%29%2F2%5C1+=+-13

Quadratic expression 1x%5E2%2B2x%2B-143 can be factored:
1x%5E2%2B2x%2B-143+=+1%28x-11%29%2A%28x--13%29
Again, the answer is: 11, -13. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-143+%29

ANSWER 1: The first odd integer is 11
x+2=11+2=13 ANSWER 2: The second odd integer is 13.
ANSWER 11+13=24 The sum of the two integers is 24.