Question

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 . Four years ago, the product of their ages in years was 48.

Answer 1

Solution:  

Given : The sum of the ages of two friends is 20 year.

Let the age of one of two friends be x yr.

Then the age of the other friend = (20 – x) yr.

4 years ago :  

Age of one of two friends = (x – 4) yr

Age of other friend = (20 – x – 4) = (16 – x) yr

A.T.Q

(x – 4) (16 – x) = 48

16x – x² – 64 + 4x = 48

– x² + 20x – 112 = 0

x² – 20x + 112 = 0

On Comparing with ax² + bx + c = 0,  

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

Discriminant,D = b² – 4ac

D = (-20)² – 4 × 112

D = 400 – 448  

D = - 48

D= - 48 < 0

b2 – 4ac < 0

Which implies that the real roots are not possible because this condition represent imaginary roots . So the solution does not exist .

Hence, the given situation is not possible.

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Answer 2

Hey mate ☺️

No, this situation is not possible as...

Hope it helps you ☺️✌️✌️