Is the following situation possible? If so,

Solution:

Let the present age of two friends be x years and (20 − x) years respectively.

Then, 4 years later, the age of two friends will be (x − 4) years and (20 − x − 4) years respectively

Then according to question,

$(x-4)(20-x-4)=48$

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

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

$-x^{2}+20 x-64-48=0$

 

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

Let D be the discriminant of the above quadratic equation.

Then,

$D=b^{2}-4 a c$

Putting the value of a = 1, b = − 20 and c = 112

$D=(-20)^{2}-4 \times 1 \times 112$

$=400-448$

 

$=-48$

Thus, $D<0$

So, the above equation does not have real roots.

Hence, the given situation is not possible.