Question

The product of two positive consecutive odd integers is 195. Create and solve an equation to find the value of the integers. What is the sum of the two integers?

Answer 1

Let's define the next variables:

x: the first odd integer

y: the next odd integer

Since they are consecutive:

x + 2 = y

The product of them is 195, then:

x*y = 195

Replacing the y from the first equation into the second one:

x*(x + 2) = 195

x*x + x*2 - 195 = 0

x² + 2x - 195 = 0

Solving with help of the quadratic formula:

`\begin{gathered} x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_(1,2)=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-195)}}{2\cdot1} \\ x_(1,2)=\frac{-2\pm\sqrt[]{784}}{2} \\ x_1=(-2+28)/(2)=13 \\ x_2=(-2-28)/(2)=-15 \end{gathered}`

Given that we are only interested in positive integers, the solution x = -15 is discarded.

Therefore, the integers are 13 and 15

The sum of them is 13 + 15 = 28