Question 12964
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