The sum of ages of Lisa and her mother is 45. The product of their ages is 126. Find their ages.

Let us say that Lisa's age ix x and her mothers age is y. Then as per the data given in the question:

x + y = 45   ...   (1)

x*y = 126   ...   (2)

Dividing both sides of equation 2 by y we get:

x = 126/y

Substituting this value of x in equation 1 we get:

126/y + y = 45

multiplying both side of above equation by y and taking all the terms on one side we get:

y^2 - 45y + 126 = 0

Therefore: y^2 - 3y - 42y + 126 = 0

Therefore: y(y - 3) - 42(y - 3) = 0

Therefore: (y - 3)*(y - 42) = 0

Therefore y = 3 or y = 42

Out of these two values 3 represents age of Lisa and 42 represents age of her mother.

Answer:

Lisa is 3 years old.

Her other is 42 years old.

NOTE: We could have found the answer by a much simpler method of trial and error of dividing the number 45 in two numbers successively as 1+44, 2+42, 3+43 and so on and calculating the product of the two components. till we get the multiplication amount as 126. As a matter of fact we have applied this method to find out factors of the equation: y^2 - 45y + 126 = 0.