Answer :
Answer:
The four page numbers were 143, 144, 145 and 146.
Step-by-step explanation:
We can assume the first page as x and the next page as x +1.
The next two facing pages would similarly be x+2 and x+3.
The sum of the numbers on the first two facing pages can be calculated as:
Sum of first two pages = x + (x + 1)
Sum of first two pages = 2x + 1
Similarly, the sum of the next two page numbers is:
Sum of next two pages = (x+2) + (x+3)
Sum of next two pages = 2x + 5
Then, we need to compute the product of the two sums.
(2x + 1) * (2x + 5)
= (2x)(2x) + (2x)(5) + (1)(2x) + (1)(5)
= 4x² + 10x + 2x + 5
= 4x² + 12x + 5
This product is equal to 80085 so,
4x² + 12x + 5 = 80085
4x² + 12x + 5 - 80085 = 0
4x² + 12x - 80080 = 0
we can solve this equation using the quadratic formula to find out the value of x. So here we have:
a = 4, b = 12, c = -80080
Using the quadratic formula:
(-b±√b²-4ac)/2a
=(-12±√(12)²-4(4)(-80080))/2(4)
=(-12±√144-(-128120))/8
=(-12±√1281424)/8
=(-12±1132)/8
= (12 + 1132)/8 or (12-1132)/8
x = 143 or -140
Since the value of x is a page number hence it can not be negative. So, we will choose the positive value i.e. 143.
We initially supposed x as the first page which the student opened. So, the first page number is 143. The next pages are:
x+1 = 143 + 1 = 144
x+2 = 143 + 2 = 145
x+3 = 143 + 3 - 146
So, the four page numbers were 143, 144, 145 and 146.