Question

4.    Is the following situation possible? If so, determine their present ages.

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

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Answer 1

Let the age of one friend = x years

∴ The age of the other friend = (20 – x – 4) years [∵ Sum of their ages is 20 years]

Four years ago

Age of one friend = (x – 4) years

Age of the other friend = (20 – x – 4) years

= (16 – x) years

According to the condition,

(x – 4) × (16 – x) = 48

⇒ 16x – 64 – x2 – 4x = 48

⇒ – x2 – 20x – 64 – 48 = 0

⇒ – x2 – 20x – 112 = 0

⇒ x2 + 20x + 112 – 0 (1)

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

∴ b2 – 4ac = (20)2 – 4 (1) (112)

= 400 – 448

= – 48 < 0

Since b2 – 4ac is Is than O.

∴ The quadratic equation (1) has no real roots.

Thus, the given equation is not possible.

Answer 2

Answer:

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