A student opens a math book to 2 facing pages. The product of the page numbers is 930. Find the page numbers.
Hint: take the square root of 930.
Thank you!
To find the page numbers, we first need to set up an equation using the given information.
Let's assume that the page numbers are represented by "x" and "x + 1". The product of the page numbers is given as 930.
So, we can write the equation as:
x * (x + 1) = 930
This is a quadratic equation. To solve it, we need to expand the equation and bring all the terms to one side:
x^2 + x - 930 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring.
We need to find two numbers that multiply to -930 and add up to 1. By trial and error, we can find that the two numbers are -30 and 31. So, we can rewrite the equation using these factors:
(x - 30)(x + 31) = 0
Now, we can set each factor equal to zero and solve for x:
(x - 30) = 0 or (x + 31) = 0
Solving these equations, we find:
x = 30 or x = -31
Since page numbers cannot be negative, we disregard -31 as a solution. Therefore, the value of x is 30.
So, the two page numbers are x = 30 and x + 1 = 30 + 1 = 31.
Hence, the page numbers are 30 and 31.