Find two consecutive positive integers such that the difference of their square is 25.
Let the first integer be n. This means the next integer is (n + 1).
Square n: n^2
Square the next consecutive integer: (n + 1)^2 = n^2 + 2n + 1
Now, we take the difference of their squares and set it equal to 25:
(n^2 + 2n + 1) - n^2 = 25
Cancelling the n^2, we get:
2n + 1 = 25
Typing this equation into our search engine, we get:
n = 12
Let the first integer be n. This means the next integer is (n + 1).
Square n: n^2
Square the next consecutive integer: (n + 1)^2 = n^2 + 2n + 1
Now, we take the difference of their squares and set it equal to 25:
(n^2 + 2n + 1) - n^2 = 25
Cancelling the n^2, we get:
2n + 1 = 25
Typing this equation into our search engine, we get:
n = 12