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

Let the left page number be x because the pages of books are numbered sequentially. 

So, Page (x + 1) will be the right page number. 

As given, the Sum of the squares of the pages is 481.

So, According to the given question:

=> x² + (x + 1)² = 481

=> x² + x² + 2x + 1 = 481

=> 2x² + 2x - 480 = 0

=> x² + x - 240 = 0

=> x² + 16x - 15x - 240 = 0

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

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

=> x = 15, - 16

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

Hence, The two-page numbers are 15 and 16.