Question

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.

Answer 1

Let the age of one friend be x years.
then the age of the other friend will be (20 - x) years.
4 years ago,
Age of 1st friend = (x - 4) years
Age of 2nd friend = (20 - x - 4) = (16 - x) years
According to question,
(x - 4) (16 - x) = 48
$16x-x^2-64+4x=48$
$-x^2+20x-112=0$
$x^2-20x+112=0$
Comparing this equation with $a{x}^2+bx+c=0$, we get
$a=1,b=-20andc=112Discriminant=b^2-4ac=(-20{)}^2-4\times 112=400-448=-48b^2-4ac<0$
Therefore, there will be no real solution possible for the equations. The given situation is not possible.