A student opens a mathmatics book to two facing pages. The product of the page numbers is 2352. Find the page numbers.
X * (X+1) = 2352
X^2 + X - 2352 = 0
Factor 2352 => 2 * 2 * 2 * 2 * 7 * 7 * 3
Since the third term is negative and the middle term is factored into 1 * X, combine the factors into two products that differ by 1.
2 * 2 * 2 * 2 * 3 = 48
7 * 7 = 49
Thus (X + 49)(X - 48) = 0
X = -49 or
X = 48
Since the page number cannot be negative, X = 48 and X + 1 = 49.
I hope this helps you to understand the process. Thanks for asking.
To find the page numbers, we need to determine two consecutive numbers whose product is 2352.
We can start by finding the factors of 2352. The factors are the pairs of numbers that multiply together to give the original number.
The factors of 2352 are:
1 × 2352 = 2352
2 × 1176 = 2352
3 × 784 = 2352
4 × 588 = 2352
6 × 392 = 2352
7 × 336 = 2352
8 × 294 = 2352
9 × 261 = 2352
12 × 196 = 2352
13 × 181 = 2352
14 × 168 = 2352
16 × 147 = 2352
18 × 131 = 2352
21 × 112 = 2352
24 × 98 = 2352
28 × 84 = 2352
33 × 71 = 2352
36 × 65 = 2352
39 × 60 = 2352
42 × 56 = 2352
48 × 49 = 2352
Now we can observe the pairs of factors and identify the consecutive numbers. The pair that represents the two consecutive page numbers should have a difference of 1.
Looking at the factors, we can see that 48 and 49 have a difference of 1. Therefore, the two facing page numbers are 48 and 49.