Answer :

Let the age of one friend be *x* years.

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

4 years ago,

age of 1^{st} friend = (*x* − 4) years

And, age of 2^{nd} 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

Comparing this equation with *ax*^{2} + *bx* + *c* = 0, we obtain

*a* = 1, *b* = −20, *c* = 112

Discriminant = *b*^{2} − 4*ac* = (− 20)^{2} − 4 (1) (112) = 400 − 448 = −48

As *b*^{2} − 4*ac* < 0,

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

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