Question

The product of two consecutvie positive odd number is 195.find the numbers

Answer 1

`13` and
`15`.

Explanation:

The difference between two consecutive odd integers is
`2`.

Let
`x` denote the smaller one of the two numbers (
`x > 0`.) The other number would be
`(x + 2)`.

`x \, (x + 2) = 195`.

Thus,
`x^(2) + 2\, x - 195 = 0`.

Solve this equation for
`x` using the quadratic formula:

`\begin{aligned}x_(1) &= \frac{-2 + \sqrt{2^(2) - 4* (-195)}}{2} \\ &= (-2 + √(784))/(2) \\ &= (-2 + 28)/(2) \\ &= 13\end{aligned}`.

`\begin{aligned}x_(2) &= \frac{-2 - \sqrt{2^(2) - 4* (-195)}}{2}\\ &= (-2 - 28)/(2) \\ &= -15\end{aligned}`.

Only
`x_(1) = 13` is a valid solution since
`x > 0` by assumption.

Therefore, the smaller one of the two odd numbers would be
`13`. The other integer would be
`13 + 2 = 15`.