Question

The product of two consecutive pages in a book is 1122.
Find the page numbers.​

Answer 1

Question :-

The product of two consective pages in a book is 1122. Find the page numbers.

Given :-

Product of two consecutive pages = 1122

To find :-

The two page numbers.

Solution :-

Let consecutive no. be x and x + 1

According to question,

product of these no. = 1122

x ( x + 1) = 1122

x² + x = 1122

x² + x - 1122 = 0

x² + 34x - 33x -1122 = 0

x( x + 34) - 33( x + 34) = 0

( x - 33) ( x + 34) = 0

x - 33 = 0 | x + 34 = 0

x = 33 | x = - 34 .

we take x = 33

Then, 1st consecutive page no. = 33.

2nd consecutive page no. = x + 1

= 33 + 1 = 34.

Final solution :-

Therefore, the page numbers are 33 and 34.

[ Note - Page no. can't be negative so negative sign gonna ignore. ]

Answer 2

Let both the number be x and x + 1

then ,

x (x + 1) = 1122

x² + x = 1122

x² + x - 1122= 0

x² + 34x - 33x - 1122 = 0

x(x + 34 ) -33(x + 34) = 0

x - 33 = 0

x = 33

x + 34 = 0

x = -34

Rejecting the negative value...

so the consecutive numbers are 33 and 33 + 1 = 34