A student opens a mathmatics book to two facing pages. The product of the page numbers is 1640.?

Let x be the lower page number

Let (x+1) be the next page number.

x(x+1) = 1640

x^2 + x = 1640

x^2 + x - 1640 = 0

(x-40)(x+41) = 0

x = -41 or x = 40

x = -41 is inadmissible

therefore, the page numbers are 40 and 41

From the problem we know that:

x * y = 1640 Where x left page and y = right page.

We also know that:

x+1 = y Substituting x + 1 for y in the first equation gives us:

x * (x+1) = 1640 Do math on left side:

x^2 + x = 1640 Put in quadratic form

x^2 + x -1640 = 0 Using the quadratic equation we get:

(-1 +/- sqr(1^2 - 4 * 1 * -1640)/2 * 1 or

(-1 +/- sqrt(6561))/2 or

(-1 +/- 81) / 2 Which gives us two answers:

(-1 - 81)/2 or

- 42 which we can ignore as you cant have negative page numbers

We also get:

(-1+81)/2 = 40 Which gives us the value of x the first page.

Adding 1 to that we get 41, the second page.

Long answer for a simple question.

Let x = first page

Let x + 1 = second page

x(x + 1) = 1640

x^2 + x - 1640

(x + 41)(x - 40) = 0

x = -41, 40

since page numbers are not negative, x = 40

The second page is x + 1 = 41

The page numbers are 40 and 41.

x = first page y = second page Since both pages are opposite to each other, they are consecutive, so the second page is 1 number greater than the first. x + 1 = y xy = 272 Now sub in (x + 1) into y in the second equation x(x + 1) = 272 x^2 + x = 272 x^2 + x - 272 = 0 (x - 16) (x + 17) = 0 x = 16 Or -17, since there is no such things as negative page numbers, disregard -17. x = 16 16 + 1 = y y = 17. First page = 16 Second page = 17

40

41

40 X 41 = 1640

40 and 41

40 and 41

x(x+1)=1640

x^2+x-1640=0

(x+41)(x-40)=0

Your page numbers are 40 and 41.