SOLUTION: if the product of two consecutive odd integers is decreased by one third the lessre the integer, the result is 250. find the integers.

Algebra ->  College  -> Linear Algebra -> SOLUTION: if the product of two consecutive odd integers is decreased by one third the lessre the integer, the result is 250. find the integers.      Log On


   

Question 36820: if the product of two consecutive odd integers is decreased by one third the lessre the integer, the result is 250. find the integers.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if the product of two consecutive odd integers is decreased by one third the lessre the integer, the result is 250. find the integers.
Let the lesser integer be "x"
Then the larger interger is "x+2"
EQUATION:
x(x+2)-(1/3)x=250
x^2+(5/3)x-250=0
3x^2+5x-750=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B5x%2B-750+=+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=%285%29%5E2-4%2A3%2A-750=9025.

Discriminant d=9025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+9025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+9025+%29%29%2F2%5C3+=+15
x%5B2%5D+=+%28-%285%29-sqrt%28+9025+%29%29%2F2%5C3+=+-16.6666666666667

Quadratic expression 3x%5E2%2B5x%2B-750 can be factored:
3x%5E2%2B5x%2B-750+=+3%28x-15%29%2A%28x--16.6666666666667%29
Again, the answer is: 15, -16.6666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B5%2Ax%2B-750+%29

Hope this helps.
Cheers,
Stan H.