SOLUTION: A student opens a mathematics book to two facing pages. The product of the page numbers is 1482. Find the page numbers. First page is _ Second page is _

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Question 156137: A student opens a mathematics book to two facing pages. The product of the page numbers is 1482. Find the page numbers.
First page is _
Second page is _
Found 2 solutions by checkley77, jim_thompson5910:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X(X+1)=1482
X^2+X-1482=0
(X+39)(X-38)=
X-38=0
X=38 FOR THE SMALLER INTEGER.
38+1=39 FOR THE SECOND INTEGER.
PROOF:
38*39=1482
1482=1482

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the pages are next to each other this means that the first page is "x" and the second page is "x+1". Because the "product of the page numbers is 1482", this means that x%28x%2B1%29=1482


x%28x%2B1%29=1482 Start with the given equation


x%5E2%2Bx=1482 Distribute


x%5E2%2Bx-1482=0 Subtract 1482 from both sides


%28x%2B39%29%28x-38%29=0 Factor the left side


x%2B39=0 or x-38=0 Set each factor equal to zero


x=-39 or x=38 Solve for "x" in each case


Ignoring the negative answer (you cannot have a negative page number), the only solution is x=38

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Answer:

So the first page is 38 and the second page is 39


Check:

38*39=1482
1482=1482 ... works