SOLUTION: Find two consecutive integers such that the sum of their squares is 61. ( The object is not to play with various consecutive-integer combinations until coming up with the solution

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Question 12964: Find two consecutive integers such that the sum of their squares is 61. ( The object is not to play with various consecutive-integer combinations until coming up with the solution (which is five and six) but to decide what the unknown (x,say) should represent, develop an equation that involves the unknown and utilizes the information provided, and solve that equation.
Answer by askmemath(368) (Show Source):
You can put this solution on YOUR website!
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