Find two consecutive integers such that the sum of their squares is 61
Smaller consecutive integer = N
Larger consecutive integer N+!
sum of their squares is 61
N² + (N+1)² = 61
N² + (N+1)(N+1) = 61
N² + (N² + N + N + 1) = 61
N² + N² + 2N + 1 = 61
2N² + 2N + 1 = 61
Get 0 on the right:
2N² + 2N - 60 = 0
Divide every term by 2
N² + N - 30 = 0
Factor:
(N + 6)(N - 5) = 0
Use zero factor principle:
N + 6 = 0; N - 5 = 0
N = -6 N = 5
Using answer N = -6
Smaller consecutive integer = N = -6
Larger consecutive integer N+1 = -6+1 = -5
Using answer N = 5
Smaller consecutive integer = N = 5
Larger consecutive integer N+1 = 5+1 = 6
Two answers: -6 and -5, or 5 and 6
Edwin