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The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Answer :

Ans. Let age of first friend = x years and let age of second friend = (20 - x) years

Four years ago, age of first friend = (x - 4) years

Four years ago, age of second friend = (20 - x) - 4 = (16 - x) years

According to given condition,

\(\Rightarrow(x - 4) (16 - x) = 48\)

\(\Rightarrow 16x - x^2 - 64 + 4x = 48\)

\(\Rightarrow 20x - x^2 - 112 = 0\)

\(\Rightarrow x^2 - 20x + 112 = 0\)

Comparing equation , \(x^2 - 20x + 112 = 0\) with general quadratic equation \(ax^2 + bx + c = 0\),

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

Discriminant = \( b^2 - 4ac \)

\( = (-20)^2 - 4 (1) (112) \)

\( = 400 – 448\) = -48 < 0\)

Discriminant is less than zero which means we have no real roots for this equation.

Therefore, the give situation is not possible.

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