Question

The product of two consective 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. ]

Thank you.

Answer 2

Step-by-step explanation:

Let the page numbers be x and x+1

ATQ

$\\\qquad\qquad\sf {:}\longrightarrow x (x+1)=1122$

$\\\qquad\qquad\sf {:}\longrightarrow x^2+x=1122$

$\\\qquad\qquad\sf {:}\longrightarrow x^2-x-1122=0$

• use mid term factorisation

$\\\qquad\qquad\sf {:}\longrightarrow x^2+34x-33x-1122=0$

$\\\qquad\qquad\sf {:}\longrightarrow x (x+34)-33 (x+34)=0$

$\\\qquad\qquad\sf {:}\longrightarrow (x+34)(x-33)=0$

$\\\qquad\qquad\sf {:}\longrightarrow x=-34 \:or\:x=33$

• Page number can't be negative

Hence the page numbers are 33 and 34.