The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is 1/3. Find her present age.
Let the present age of Meena be x years
Meena’s age three years ago = (x – 3) years
Meena’s age five years hence = (x + 5) years
According to given question
x2 + 2x – 15 = 6x + 6
x2 – 4x – 21 = 0
Using the splitting middle term – the middle term of the general equation is divided in two such values that:
Product = a.c
For the given equation a = 1 b = – 4 c = – 21
= 1. – 21 = – 21
And either of their sum or difference = b
= – 4
Thus the two terms are – 7 and 3
Sum = – 7 + 3 = – 4
Product = – 7.3 = – 21
x2 – 7x + 3x – 21 = 0
x (x – 7) + 3(x – 7) = 0
(x – 7) (x + 3) = 0
x = – 3 or x = 7
x = 7 age cannot be negative
Hence the present age of Meena is 7 years