# Is the following situation possible? If so,

Question:

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

Solution:

Let the present age of two friends be x years and (20 − x) years respectively.

Then, 4 years later, the age of two friends will be (x − 4) years and (20 − x − 4) years respectively

Then according to question,

$(x-4)(20-x-4)=48$

$(x-4)(16-x)=48$

$16 x-x^{2}-64+4 x=48$

$-x^{2}+20 x-64-48=0$

$x^{2}-20 x+112=0$

Let D be the discriminant of the above quadratic equation.

Then,

$D=b^{2}-4 a c$

Putting the value of a = 1, b = − 20 and c = 112

$D=(-20)^{2}-4 \times 1 \times 112$

$=400-448$

$=-48$

Thus, $D<0$

So, the above equation does not have real roots.

Hence, the given situation is not possible.