SOLUTION: A student opens a book with two facing pages. The product of the page numbers is 1056 find the page numbers.

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Question 367099: A student opens a book with two facing pages. The product of the page numbers is 1056 find the page numbers.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = one of the facing pages.
let y = the other of the facing pages.

it's clear that y has to be equal to x + 1, so your 2 pages are therefore equal to:

x and (x+1)

the product of these 2 pages is equal to 1056

this means that:

x * (x+1) = 1056

simplify to get:

x^2 + x = 1056

subtract 1056 from both sides of this equation to get:

x^2 + x - 1056 a= 0

your factors for this quadratic equation are:

(x - 32) * (x + 33) = 0 because:

32*33 = 1056
33 - 32 = 1

you get:

x = 32 or x = -33

x can't be -33, so x = 32 is your answer.

you get:

x = 32
x + 1 = 33

page 32 faces page 33.

32 * 33 = 1056.

there's your answer.