Question

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

Answer 1

Answer:

$13$ and $15$.

Step-by-step 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:

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

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

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 $13 + 2 = 15$.