Question

Make up a problem involving the product of two

consecutive even integers. Start by choosing two

consecutive odd integers.

a) What are your integers?

b) What is the product of your integers?

c) Solve the equation n(n + 2) = p , where p is the product you found in part (b).

d) Did you get the numbers you started with?

Short answer

a) 3 and 5

b) 15

c) $n_1=3,n_2=-5$

d) No

Step-by-step solution

Step 1. Given Information 

Any random two consecutive odd numbers and Equation : n(n + 2) = p

Part (a) Step 2. Choosing integers

Let the two consecutive odd integers are :

x = 3, y = 5

Part (b) Step 3. Product of integers

Product of integers :

$$\begin{gathered} =x*y \\ =3*5 \\ =15 \end{gathered}$$

Part (c) Step 4. Solving the equation

$$\begin{gathered} p=15 \\ \mathrm{Equation}:n(n+2)=p \\ n(n+2)=15 \\ {n}^2+2n-15=0 \\ (n+5)(n-3)=0 \\ n+5=0,n-3=0 \\ \mathrm{Therefore},n_1=-5\mathrm{and}{n}_2=3 \end{gathered}$$

Part (d) Step 5. Explanation.

Integers selected : 3 and 5

Integers on solving equation : 3 and -5

Hence, the integers we get on solving equation are not same as the ones selected.