Question

Find two consecutive integers such that the sum of their squares is 61

Answer 1

Since they are consecutive numbers, one number is bigger than the other by 1. 
So if 1 number is X the other number is X+1 
Squares are X^2 and (X+1)^2 
Sum of squares = X^2+(X+1)^2 = 61 
X^2+X^2 + 2X +1 = 61 
2X^2 + 2X =60
X^2 + X = 30
Here's a shortcut
Taking X common we get
X(X+1) = 30
Factors of 30 include 5 and 6
X(X+1) = 5x6 
So X = 5 and X+1 = 6 
Check:
Squaring 6^2 = 36 and 5^2 = 25
Sum = 36+25 = 61 

Answer 2

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