Question

The sum of the ages of two friends is 20 yeras. Four years ago the prosuct of their ages was 48. Show that thses statements can not be true.

Answer 1

Let the age of one friend be x years.

Age of the other friend will be (20 − x) years.

4 years ago, age of 1st friend = (x − 4) years

And, age of 2nd friend = (20 − x − 4)

= (16 − x) years

Given that,

(x − 4) (16 − x) = 48

16x − 64 − x2 + 4x = 48

− x2 + 20x − 112 = 0

x2 − 20x + 112 = 0

Comparing this equation with ax2 + bx + c = 0, we obtain

a = 1, b = −20, c = 112

Discriminant = b2 − 4ac = (− 20)2 − 4 (1) (112)

= 400 − 448 = −48

As b2 − 4ac < 0,

Therefore, no real root is possible for this equation and hence, this situation is not possible.

hope you understand it