SOLUTION: Can someone help me solve this problem. A student opens a math book to 2 facing pages. The product of the page number is 1056. Find the page numbers. Thank you.

Question 132292: Can someone help me solve this problem.
A student opens a math book to 2 facing pages. The product of the page number is 1056. Find the page numbers.
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If we look at the page numbers, we'll notice that they are consecutive integers. So they follow the algebraic form , , , etc.

So if the product of two consecutive integers is 1056, then we have the equation

Distribute

Subtract 1,056 from both sides

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our possible solutions are

or

However, since a negative page number is not possible, this means that the only solution is

Now to find the next page number, simply add 1 to 32 to get

So the two page numbers are 32 and 33

Check:

To check this answer, simply multiply the two numbers:

Works.
RELATED QUESTIONS
A student opens a math book to two facing pages the product of the page number is 110.... (answered by Alan3354)

Please help solve I am very confused with this problem. A student opens a book to 2... (answered by jim_thompson5910)

A student opens a math book to two facing pages. The product of the page number is 506.... (answered by rfer)

a student opens a mathematics book to two facing pages. The product of the page numbers... (answered by jim_thompson5910)

Can you help me solve this problem that I am confused with. A student opens a... (answered by jjordan95)

A student opens a mathematics book to two facing pages. the product of the page numbers... (answered by richard1234)

Word problem: A student opens a math book to two facing pages. The product of page... (answered by ewatrrr)

A student opens his math book to two facing pages. The product of the page numbers is... (answered by solver91311)

A student opens a mathematic book to two facing pages he product of the pages numbers... (answered by Alan3354)