Is the following situation possible?

Solution:

Let the age of one friend be x years.

Age of the other friend will be (20 – x) years.

4 years ago, age of 1st friend = (x – 4) years

And, age of 2nd friend = (20 – x – 4)

$=(16-x)$ years

Given that,

$(x-4)(16-x)=48$

$16 x-64-x^{2}+4 x=48$

$-x^{2}+20 x-112=0$

$x^{2}-20 x+112=0$

$a=1, b=-20, c=112$

Discriminant $\mathrm{D}=\mathrm{b}^{2}-4 \mathrm{ac}=(-20)^{2}-4(1)(112)$

$=400-448=-48$

As $b^{2}-4 a c<0$

Therefore, no real root is possible for this equation and hence, this situation is not possible.