The product of the page numbers on two facing pages of a book is 110. Find the page numbers. the page numbers are:
To find the page numbers, we need to set up an equation based on the given information.
Let's assume the first page number is x. Since the pages are facing each other, the second page number will be x + 1 (because the next page number is always one more than the previous one).
According to the problem, the product of these two page numbers is equal to 110. So, we can write the equation as:
x * (x + 1) = 110
Now, let's solve this equation:
x^2 + x = 110
Rearranging the equation:
x^2 + x - 110 = 0
Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. Let's use the quadratic formula, which states:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 1, and c = -110.
x = (-1 ± √(1^2 - 4(1)(-110))) / (2(1))
x = (-1 ± √(1 + 440)) / 2
x = (-1 ± √441) / 2
x = (-1 ± 21) / 2
Now we have two possible solutions for x:
1. x = (-1 + 21) / 2 = 20 / 2 = 10
2. x = (-1 - 21) / 2 = -22 / 2 = -11
Since a page number cannot be negative, we can discard -11 as a valid answer.
Therefore, the first page number is 10 and the second page number is 10 + 1 = 11.
So, the page numbers are 10 and 11.
To find the page numbers, let's assume the first page number as "x" and the second page number as "x+1". Now, we can set up the equation based on the given information, which states that the product of the page numbers is 110:
x * (x+1) = 110
Now, let's solve this equation:
x^2 + x = 110
Rearranging the equation:
x^2 + x - 110 = 0
Now, we can factorize or use the quadratic formula to solve this equation. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation x^2 + x - 110 = 0, the coefficients are:
a = 1, b = 1, c = -110
Substituting these values into the quadratic formula:
x = (-1 ± √(1^2 - 4(1)(-110))) / (2(1))
Simplifying further:
x = (-1 ± √(1 + 440)) / 2
x = (-1 ± √441) / 2
Now, let's calculate the square root:
x = (-1 ± 21) / 2
This gives us two possible solutions for x:
x1 = (-1 + 21) / 2 = 20 / 2 = 10
x2 = (-1 - 21) / 2 = -22 / 2 = -11
Since page numbers cannot be negative, we discard the x2 value. Therefore, the first page number is 10, and the second page number is x+1 = 10+1 = 11.
So, the page numbers are 10 and 11.