Question

The product of two consecutive odd integers is 168.Find the integers.

Short answer

The two consecutive odd integers is$-12and14.$

Step-by-step solution

Given Information 

The product of two consecutive odd integers is 168.

Solve the equation 

Take n = the first odd integer

n + 1 = the next odd integer.

The product of two consecutive odd integers is 168. The product of the first odd integer and the second odd integers is 168.

$$\begin{gathered} \left(n\right)\left(n+1\right)=168 \\ {n}^2+n=168 \\ {n}^2+n-168=0 \\ a=1,b=1andc=-168 \\ U\sin gquadraticformula \\ n=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ n=\frac{-2\pm \sqrt{2^2-4\left(1\right)\left(-168\right)}}{2} \\ n=\frac{-2\pm 26}{2} \\ n=\frac{-2-26}{2},\frac{-2+26}{2} \\ n=\frac{-28}{2},\frac{24}{2} \\ n=-14,12 \\ n+2=-14+2,12+2 \\ =-12,14 \end{gathered}$$

n = -14 +2 = -12

n = 12 + 2 = 14