Question

The sum of the ages of a boy and his elder brother is $12years$ and the sum of the square of their ages in $74$ (in years). Find their ages.

Answer 1

Let $a$ be the age of boy and $b$ be the age of his elder brother.

$a+b=12\Rightarrow a^2+b^2+2ab=144$

$a^2+b^2=74\Rightarrow 2ab=70$

$ab=35$

$a=\frac{35}{b}$

$35+b^2=12b$

$b^2-12b+35=0$

$b^2-7b-5b+35=0$

$b(b-7)-5(b-7)=0$

$(b-5)(b-7)=0$

$b=5a=7$

$b=7a=5$