Question

The product of two consecutive positive even numbers is 1,224. Find the numbers.

Answer 1

Answer:

34 and 36.

Step-by-step explanation:

By multiplying 34 by 36 (consecutive positive even numbers) we get 1,224!

Answer 2

The product of two consecutive positive even numbers is 1,224. The numbers are 34 and 36.

Solution:

Given that product of two consecutive positive even number is 1224.

Need to find the numbers

Let one even number be represented by variable x

So other consecutive even number = x + 2

As product is 1224 we can frame a equation as,

$\begin{array}{l}{\Rightarrow x(x+2)=1224} \\ {=>x^{2}+2 x=1224} \\ {=>x^{2}+2 x-1224=0}\end{array}$

we got a quadratic equation. lets solve it by quadratic formula

According to quadratic formula for general equation a$x^2$ + bx + c = 0 , solution of the equation is given by  

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\text { Our equation } x^{2}+2 x-1224$

So in our case, a = 1, b = 2 and c = -1224

On applying quadratic formula we get

$\begin{array}{l}{x=\frac{-2 \pm \sqrt{2^{2}-4 \times 1 \times(-1224)}}{2 \times 1}} \\\\ {x=\frac{-2 \pm \sqrt{4+4896}}{2}} \\\\ {x=\frac{-2 \pm \sqrt{4900}}{2}} \\\\ {x=\frac{-2 \pm 70}{2}} \\\\ {x=\frac{68}{2}=34 \text { or } x=\frac{-72}{2}=-36}\end{array}$

As required number is positive , ignoring the negative value  

x  = 34  

x + 2 = 34 + 2 = 36

Hence two positive even consecutive number having product as 1224 are 34 and 36.