Chapter 9.4, Problem 34PPS

To determine

Find the integers.

Answer to Problem 34PPS

The integers are 14 and 16 or − 16 and − 14.

Explanation of Solution

Given:

The product of two consecutive even integers is 224. Find the integers.

Concept Used:

The difference between two integers is 2.

Let the first even integer is x and the next one is x+2

Equation: $x(x+2)=224$

Calculation:

Equation: $x(x+2)=224$

Now solve for x.

  $\begin{array}{l}x(x+2)=224\\ x^2+2x=224\text{[}\text{open}\text{the}\text{parenthesis}\text{]}\\ x^2+2x-224=224-224\text{[}\text{subtract}\text{224}\text{from}\text{both}\text{sides}\text{]}\\ x^2+2x-224=0\\ (x+16)(x-14)=0\end{array}$

Now use zero product rule to find the value of x.

  $\begin{array}{l}x+16=0\text{and}x-14=0\\ x=-16\text{and}x=14\end{array}$

The integers are 14 and 16 or − 16 and − 14.

Thus, the integers are 14 and 16 or − 16 and − 14.