Question

find 2 consecutive integers such that three times the square of the first is equal to seven more than five times the second

Answer 1

Explanation:

We are looking for two numbers,
`N` and
`N + 1`. From the problem statement, we can setup the following equation:

`3N^(2) = 5(N + 1) + 7`

`3N^(2) = 5N + 5 + 7`

`3N^(2) - 5N - 12 = 0`

`(3N + 4)(N - 3)`

`N = (-4)/(3), 3`

Because 3 is the only integer solution, the answer is 3 and 4.