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.

Dear Student

Let’s say, theage of one friend be x years.

Then, the age of the other friend will be (20 - x) years.

Four years ago,

Age of First friend = (x- 4) years
Age of Second friend = (20 -x- 4) = (16 -x) years

As per the given question, we can write, (x- 4) (16 -x) = 48

16x - x^2- 64 + 4x= 48

-x^2+20x-112=0

x^2- 20x +112 = 0


Comparing the equation withax^2+bx+c= 0, we get
a=1,b= -20andc= 112

Discriminant =b^2- 4ac
=> (-20)^2- 4 × 112
=> 400 - 448 = -48

b^2- 4ac <0
Therefore, there will be no real solution possible for the equations.
Hence, condition doesn't exist.

Thanks