Two consecutive integers are squared. The sum of these squares of these squares is 545. What are the integers?

Answer 1

Fast way:
Half of 545 = 272 must fall between two perfect sequres, namely 256 and 289, which means that the integers are 16 and 17.

Standard way:
Let x be one of the integers, then x+1 is the other. So that:
x^2+(x+1)^2=545
2x^2+2x-544=0
x^2+x-272=0
(x+17)(x-16)=0
So x=16 or x=-17.
The consecutive integers are therefore:
16, 17, or
-17, -16