SOLUTION: A Student opens a mathematics book to two facing pages. The product of the page numbers is 342. What are the page numbers. The First page is The second page is Thank you for you

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A Student opens a mathematics book to two facing pages. The product of the page numbers is 342. What are the page numbers. The First page is The second page is Thank you for you      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 176175: A Student opens a mathematics book to two facing pages. The product of the page numbers is 342. What are the page numbers.
The First page is
The second page is
Thank you for your help
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the page numbers a and a+1
:
a(a+1)=342
:
a%5E2%2Ba-342=0
:
answer:system%2818%2C19%29
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-342+=+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=%281%29%5E2-4%2A1%2A-342=1369.

Discriminant d=1369 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+1369+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+1369+%29%29%2F2%5C1+=+18
x%5B2%5D+=+%28-%281%29-sqrt%28+1369+%29%29%2F2%5C1+=+-19

Quadratic expression 1x%5E2%2B1x%2B-342 can be factored:
1x%5E2%2B1x%2B-342+=+%28x-18%29%2A%28x--19%29
Again, the answer is: 18, -19. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-342+%29