Question 288
You have two consecutive integers, number and number+1. The sum of their squares is {{{number^2 + (number+1)^2}}}. Since it is 41, we have 

{{{number^2 + (number+1)^2 = 41}}} or

{{{number^2+ (number^2+2number+1) = 41}}}

or

{{{2number^2+2number -40}}}

Solve it using my quadratic solver. (the solution is pretty obvious, 4 and 5, it is just as easy to try the first few numbers without writing an equation)