Question

the sum of the ages of a father and his son is 54 years 2 years ago the product of their age is 400 find their present ages

Answer 1

let father age be x and son age be 54-x

according to question 

(x-2)(54-x-2)= 400
(x-2)(52-x)=400
52x -x2 -104 + 2x=400

x2- 54x +504=0
x = -b + sqroot of b2 -4ac/2a

+54+sqroot of 542 -4(1)(+504)
                  2
54 + sqroot of 2196-2016
               2

54+ sqroot​ of 900
          2
54 + 30
     2

x=84/2, x=24/2
x=42 or 12
12 regected as father age cannot be 12
therefore father age= x= 42
son age=54-x= 54-42=12