Let the age of one of the friends be ‘x’.
Age of another friend is (20 – x).
4 years back age of 1st friend is (x – 4)
4 years back age of 2nd friend = (20 – x – 4)
= (16 – x)
Product of their ages is 48.
∴ (x – 4) (16 – x) = 48
16x – x2 – 64 + 4x = 48
-x2 + 20x – 64 = 48
-x2 + 20x – 64 – 48 = 0
-x2 + 20x – 112 = 0
x2 – 20x + 112 = 0
Here, a = 1, b = -20, c = 112
b2 – 4ac = (-20)2 – 4( 1)( 112) = 400 – 448 = – 48
Here, b2 – 4ac = -48 < 0.
∴ It has no real roots.
∴ This situation is not possible.