Question

solve x+y=12 x(x) +y(y) =78​

Answer 1

Question : The sum of the ages of a boy and his elder brother is 12 years and the sum of the squares of their ages is 74 (in year. Find their ages.

Step-by-step explanation :

Let the ages of the boy be x years and that of his elder brother be y years, y > x.

ATQ,

x + y = 12 ..... (1)

x^2 + y^2 = 74 ..... (2)

Squaring both sides of (1), we get

(x + y)^2 = 12^2

or, x^2 + y^2 + 2xy = 144

or, 74 + 2xy = 144

or, 2xy = 70

Now, (x - y)^2 = x^2 + y^2 - 2xy

= 74 - 70

= 4

i.e., y - x = 2 ..... (3), since y > x

Adding (1) and (2), we get

x + y + y - x = 12 + 2

or, 2y = 14

or, y = 7

Putting y = 7 in (1), we get

x + 7 = 12

or, x = 12 - 7

or, x = 5

Therefore age of the boy is 5 years and that of his elder brother is 7 years.