Let, the age of the first friend = x years
So, the age of the other friend = 20 – x years
Four years ago:
Age of the first friend = x – 4 years
Age of the second friend = 20 – x – 4 = 16 – x years
According to question,
(x – 4) (16 – x) = 48
⇒ 16x – x² – 64 + 4x = 48
⇒ x² – 20x + 112 = 0
For the quadratic equation x² – 20x + 112 = 0, we have a = 1, b = – 20, c = 112.
Therefore,
D = b² – 4ac = (-20)² – 4 × 1 × 112 = 400 – 448 = – 48 < 0
So, there is no real roots of this quadratic equation.
Hence, this situation is not possible.