Question 1185012
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Let the two page numbers be n and n+1.  Note that to be page numbers in a book, the page number on the right should be odd, so n should be even and n+1 odd.<br>
Algebraically, we would need to solve the equation<br>
{{{n(n+1)=3422}}}<br>
However, trying to solve that algebraically would lead to having to find two numbers that differ by 1 and whose product is 3422.  But that's what the original problem asked us to do -- so the formal algebra doesn't help us.<br>
Instead we can find the answer by trial and error, but with logical analysis.<br>
The two numbers differ by 1, so the product 3422 is close to a perfect square; a "nice" perfect square close to 3422 is 60^2=3600.  So the two numbers n and n+1 should be just under 60.<br>
And to get a product with units digit 2 by multiplying two consecutive integers that are a bit less than 60, the only possibility is 58*59.  And performing that calculation confirms that the product is indeed 3422.<br>
So the two page numbers are 58 and 59.<br>
ANSWER: The sum of the two page numbers is 58+59=117<br>