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Answer :
To find the page numbers that Kylie sees, let's define the situation:
When a book is opened, two pages are visible, typically one with an even page number and the next page with an odd page number. Let's assume [tex]\( x \)[/tex] represents the first page number, and since page numbers are consecutive, the next page number will be [tex]\( x + 1 \)[/tex].
According to the problem, the product of these two consecutive page numbers is 156. Mathematically, we can express this as:
[tex]\[ x(x + 1) = 156 \][/tex]
This is the equation that represents the situation given in the problem.
Now, let's solve this equation:
[tex]\[ x(x + 1) = 156 \][/tex]
Expanding it, we get:
[tex]\[ x^2 + x = 156 \][/tex]
Rearranging terms gives us a standard quadratic equation:
[tex]\[ x^2 + x - 156 = 0 \][/tex]
To solve this quadratic equation, we can use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = -156 \)[/tex].
Calculating the discriminant:
[tex]\[ b^2 - 4ac = 1^2 - 4 \times 1 \times (-156) = 1 + 624 = 625 \][/tex]
The square root of 625 is 25. Now substitute back into the quadratic formula:
[tex]\[ x = \frac{-1 \pm 25}{2} \][/tex]
This gives two potential solutions:
1. [tex]\( x = \frac{-1 + 25}{2} = \frac{24}{2} = 12 \)[/tex]
2. [tex]\( x = \frac{-1 - 25}{2} = \frac{-26}{2} = -13 \)[/tex]
Since a page number cannot be negative, we discard [tex]\( x = -13 \)[/tex] as a possible solution.
Thus, the page number Kylie is looking at is 12, and the next page would be 13. Therefore, the correct equation from the options given is:
(4) [tex]\( x(x+1) = 156 \)[/tex]
When a book is opened, two pages are visible, typically one with an even page number and the next page with an odd page number. Let's assume [tex]\( x \)[/tex] represents the first page number, and since page numbers are consecutive, the next page number will be [tex]\( x + 1 \)[/tex].
According to the problem, the product of these two consecutive page numbers is 156. Mathematically, we can express this as:
[tex]\[ x(x + 1) = 156 \][/tex]
This is the equation that represents the situation given in the problem.
Now, let's solve this equation:
[tex]\[ x(x + 1) = 156 \][/tex]
Expanding it, we get:
[tex]\[ x^2 + x = 156 \][/tex]
Rearranging terms gives us a standard quadratic equation:
[tex]\[ x^2 + x - 156 = 0 \][/tex]
To solve this quadratic equation, we can use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = -156 \)[/tex].
Calculating the discriminant:
[tex]\[ b^2 - 4ac = 1^2 - 4 \times 1 \times (-156) = 1 + 624 = 625 \][/tex]
The square root of 625 is 25. Now substitute back into the quadratic formula:
[tex]\[ x = \frac{-1 \pm 25}{2} \][/tex]
This gives two potential solutions:
1. [tex]\( x = \frac{-1 + 25}{2} = \frac{24}{2} = 12 \)[/tex]
2. [tex]\( x = \frac{-1 - 25}{2} = \frac{-26}{2} = -13 \)[/tex]
Since a page number cannot be negative, we discard [tex]\( x = -13 \)[/tex] as a possible solution.
Thus, the page number Kylie is looking at is 12, and the next page would be 13. Therefore, the correct equation from the options given is:
(4) [tex]\( x(x+1) = 156 \)[/tex]
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