Question

If two numbers differ by 3 and their product is 504, then the numbers are

• A. 21, 24 or $-24$, $-21$
• B. 30, 31 or $-30$, $-31$
• C. 40, 41 or $-40$, $-41$
• D. none of these

Answer 1

The correct option is A 21, 24 or $-24$, $-21$

Difference between two numbers is 3

Let one number be x, other number will be x+3

Product of two numbers is 504

It implies that,

$\left(x\right)(x+3)=504$

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

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

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

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

$\Rightarrow (x-21)=0or(x+24)=0$

therefre x=21 or -24