Q. 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.

Ans: (note: In this question, we justify the answer with proper reason)

Let’s consider the ages of friends as X years and Y years.

By given 1st condition: Sum of the ages of two friends is 20 years

………….(i)

By given 2nd condition: Four years ago, the product of their ages in years was 48:

.… (ii)

By substituting value of X from equation (i) into equation (ii), we get:

Here, clear factors are not possible, let’s check by discriminant method:

By comparing the equation with standard quadratic equation a x2 + b x + c = 0,

we get: a = 1, b = – 20, c = 112

Next, we check its discriminant b2 – 4 a c:

So, b2 – 4 a c = (-20)2 – 4 (1) (112) = 400 – 448 = – 48 < 0

Since the square of a real number can not be negative, therefore will not  have any real value.

Therefore, the quadratic equation Y2 – 20 Y + 112 = 0 will not have any real roots.

Therefore, the value of present ages of two friends in given situation can not be determined.

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