Find two consecutive integers if the sum of their squares is 1513
Let the first integer be n. The next consecutive integer is (n + 1).
The sum of their squares is:
n^2 + (n + 1)^2 = 1513
n^2 + n^2 + 2n + 1 = 1513
2n^2 + 2n + 1 = 1513
Subtract 1513 from each side:
2n^2 + 2n - 1512 = 0
We have a quadratic equation. We type this into our search engine and get:
n = (-27, 28)
Let's take the positive solution.
The second integer is: n + 1
28 + 1 = 29
Let the first integer be n. The next consecutive integer is (n + 1).
The sum of their squares is:
n^2 + (n + 1)^2 = 1513
n^2 + n^2 + 2n + 1 = 1513
2n^2 + 2n + 1 = 1513
Subtract 1513 from each side:
2n^2 + 2n - 1512 = 0
We have a quadratic equation. We type this into our search engine and get:
n = (-27, 28)
Let's take the positive solution.
The second integer is: n + 1
28 + 1 = 29