Two numbers differ by 3 and their product is 504. Find the numbers.

Given:

Two numbers differ by 3 and their product is 504.

 To do:

We have to find the numbers.

Solution:

Let the two numbers be $x$ and $x+3$.

According to the question,

$x(x+3)=504$

$x^2+3x=504$

$x^2+3x-504=0$

Solving for $x$ by factorization method, we get,

$x^2+24x-21x-504=0$

$x(x+24)-21(x+24)=0$

$(x+24)(x-21)=0$

$x+24=0$ or $x-21=0$

$x=-24$ or $x=21$

If $x=-24$, then $x+3=-24+3=-21$

If $x=21$, then $x+3=21+3=24$

The required numbers are $-24$ and $-21$ or $21$ and $24$. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

198 Views

Kickstart Your Career

Get certified by completing the course

Get Started