# Q4.    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.

Let the age of one friend be $x\ years.$

and the age of another friend will be: $(20-x)\ years.$

4 years ago, their ages were, $x-4\ years$ and $20-x-4 \ years$.

According to the question, the product of their ages in years was 48.

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

$\Rightarrow 16x-64-x^2+4x= 48$

$\Rightarrow -x^2+20x-112 = 0$  or  $\Rightarrow x^2-20x+112 = 0$

Now, comparing to get the values of $a,\ b,\ c$.

$a = 1,\ b= -20,\ c =112$

Discriminant value $D = b^2-4ac = (-20)^2 -4(1)(112) = 400-448 = -48$

As $D<0$.

Therefore, there are no real roots possible for this given equation and hence,

This situation is NOT possible.

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