Question

Find two consecutive even numbers whose product is$624$.

Short answer

The pair of consecutive numbers are$-24,-26$and$24,26$.

Step-by-step solution

Step 1. Given information.

Two consecutive even numbers whose product is$84$.

Step 2. Find two consecutive even numbers.

Let the first even number is $x$.

Thus, the second number is $x+2$.

$\begin{array}{rcl}x\left(x+2\right)& =& 624\\ x^2+2x& =& 624\\ x^2+2x-624& =& 0\end{array}$

Step 3. Solve the equation.

$\begin{array}{rcl}{x}^2+2x-624& =& 0\\ x^2+26x-24x-624& =& 0\\ x\left(x+26\right)-24\left(x+26\right)& =& 0\\ \left(x+26\right)\left(x-24\right)& =& 0\end{array}$

Step 4. Apply zero product property and solve for x.

$\begin{array}{rcl}x+26& =& 0\\ x& =& -26\end{array}$ and $\begin{array}{rcl}x-24& =& 0\\ x& =& 24\end{array}$

Hence, the first pair of consecutive numbers are $-26$and $-26+2=-24$.

The second pair of consecutive numbers are $24$and$24+2=26$.