Question

the sum of the age of a boy and his elder brother is 12years and the sum of the square of their ages in 74(inyears).find their ages.

Answer 1

x + y = 12

x² + y² = 74

(x + y)² = x² + y² + 2xy

12² = 74 + 2xy

2xy = 144 - 74

xy = 70/2 = 35

If x+y =12,  x = 12 -y

so  (12 -y)y = 35

12y - y² = 35

y² - 12y + 35 = 0

(y - 7) (y - 5) = 0

y = 7, 5

If y = 7 then x = 12 - 7 = 5

If y = 5  then x = 12 - 5 = 7

So boy's age = 5 years

His elder brother's age = 7 years