Two natural numbers are such that they differ by 2, and their product is 48. Find the numbers.

Given :

Difference between two natural numbers is 2.

Product of the numbers is 48.
 

To find :

We have to find the numbers.

Solution :

Let the smaller number be 'x'.

Since the numbers differs by 2, let the greater number be $x+2$

Product of the numbers,

$x \times (x+2) = 48$

$x^2 + 2x = 48$

$x^2 + 2 x - 48 = 0$

Split the middle term into two terms, such that, 

Their sum will be $2$, and their product will be $-48$.

$x^2 + 8x - 6x - 48 = 0$                 $[8 - 6 = 2 ; 8 \times (-2) = -48]$

$x(x + 8) - 6 (x + 8) = 0$

$(x + 8) (x - 6) = 0$

$x = -8 , x = 6$

Natura number should be positive, so $x = 6$.

Greater number $= x + 2 = 6 + 2 = 8$.

Therefore, the natural numbers are 6 and 8. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

102 Views

Kickstart Your Career

Get certified by completing the course

Get Started