Let’s say, the age of one friend be x years.

Then, the age of the other friend will be (20 – x) years.

Four years ago,

Age of First friend = (x – 4) years

Age of Second friend = (20 – x – 4) = (16 – x) years

As per the given question, we can write,

(x – 4) (16 – x) = 48

16x – x^{2} – 64 + 4x = 48

– x^{2} + 20x – 112 = 0

x^{2} – 20x + 112 = 0

Comparing the equation with ax^{2} + bx + c = 0, we get

a = 1, b = -20 and c = 112

Discriminant = b^{2} – 4ac

= (-20)^{2} – 4 × 112

= 400 – 448 = -48

b^{2} – 4ac < 0

Therefore, there will be no real solution possible for the equations. Hence, condition doesn’t exist.

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