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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, 16I 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»

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.


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