The sum of the squares of two consecutive numbers is 145. Find the numbers.

The sum of the squares of two consecutive numbers is
145.

Let the numbers be N and N +
1

Now we have N^2 + (N +1)^2 =
145

=> N^2 + N^2 + 2N + 1 =
145

=> 2N^2 + 2N - 144 =
0

=> N^2 + N - 72 =
0

=> N^2 + 9N - 8N - 72 =
0

=> N(N + 9) - 8(N + 9) =
0

=> (N - 8)(N + 9) =
0

N can be 8 or
-9

So the two numbers are (8 , 9) or ( -8 ,
-9).