a student opens a book to two facing pages the product of the page numbers is 812, find the page numbers.
n(n+1) = 812
n^2 +1 - 812 = 0
(n-28)(n+29) = 0
28 and 29
To find the page numbers, we need to set up an equation based on the given information.
Let's assume that the student opens the book to page "x" and the next page is "x + 1". The product of the page numbers is 812, so we can write the equation as:
x * (x + 1) = 812
To solve this equation, we can start by simplifying it:
x^2 + x = 812
Rearranging the equation to get a quadratic equation in standard form:
x^2 + x - 812 = 0
Now we can solve this quadratic equation. There are different methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.
In this case, let's use factoring to find the page numbers. We need to find two numbers whose product is -812 and whose sum is 1.
Factors of 812: 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
By examining these factors, we see that 28 and 29 have a sum of 57. Therefore, the two page numbers are:
x = 28
x + 1 = 29
So, the student has opened the book to pages 28 and 29.