Question

The sum of the squares of the left and right pages of a book is 481. What are the page numbers?

(a) 11, 12

(b) 12, 13

(c) 17, 18

(d) 15, 16

I have been asked this question by my college director while I was bunking the class.

This is a very interesting question from Solution of Quadratic Equation by Factorisation topic in section Quadratic Equation of Mathematics – Class 10

Answer 1

Correct option is (d) 15, 16

To explain I would say: Since the pages of books are consecutive numbers, so let the left page number be x. The right page number will be x+1.

Sum of the squares of the pages is 481

x^2+(x+1)^2=481

x^2+x^2+1+2x=481

2x^2+2x-480=0

x^2+x-240=0

x^2+16x-15x-240=0

x(x+16)-15(x+16)=0

(x-15)(x+16)=0

x=15, -16

Since, page number cannot be negative, so x=15

The two page numbers are 15 and 16.