Let the present age of friend 1 be a x years
Given that,
Sum of the ages of two friends = 20 years
⇒ Present age of friend 2 = (20 – x) years
And also given that, four years ago, the product of their age was 48.
⇒ Age of friend 1 before 4 years = (x – 4) years
And age of friend 2 before 4 years = (20 – x – 4) years = (16 – x) years
Given that,
( − 4)(16 − ) = 48
⇒ 16 − 2 − 64 + 4 = 48
⇒ 2 − 20 + 112 = 0
Let D be the discriminant of this quadratic equation.
Then, D = (−20)2 − 4 × 112 × 1 = 400 − 448 = −48<0
We know that, to have real roots for a quadratic equation that discriminant D must be
greater than or equal to 0 i.e. D ≥ 0
But D< 0 in the above. So, above equation does not have real roots
Hence, the given situation is not possible.