X^2+(x+1)^2=61, x=5. The Two Consecutive Integers is 5 and 6.

Let n be the first consecutive integer

n+1 is the other consecutive integer

"The sum of the square of two consecutive integers is 61" n^2 + (n+1)^2=61

n^2 + n^2 +2n +1 =60

2n^2 +2n - 60 = 0

n^2 + n - 30 = 0

we can quadratic formula to the answer, or we can use "complete square method" to find the answer

Or we can factor n^2 + n - 30 =0 (n - 6)(n + 5) = 0

therefore, n = 6 and n = 5

n+1 is the other consecutive integer

"The sum of the square of two consecutive integers is 61" n^2 + (n+1)^2=61

n^2 + n^2 +2n +1 =60

2n^2 +2n - 60 = 0

n^2 + n - 30 = 0

we can quadratic formula to the answer, or we can use "complete square method" to find the answer

Or we can factor n^2 + n - 30 =0 (n - 6)(n + 5) = 0

therefore, n = 6 and n = 5