Question

The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.

Answer 1

Let the age of boy be x and the age of his brother be y
then
$x+y=25$.....(1)
and
$xy=126$.....(2)
then
$(x-y{)}^2=(x+y{)}^2-4xy$
$x-y=\sqrt{(x+y{)}^2-4xy}$
$x-y=\sqrt{\left(25\right)2-4\times 126}$
$x-y=\sqrt{625-504}$
$x-y=\sqrt{121}=11$
$x-y=11$....(3)

from equation (1) and (3)
$x+y=25$....(1)
$x-y=11$.....(3)
Adding them
$2x=36$
$x=18$
put in equation (1)
$18+y=25$
$y=25-18$
$y=7$

answer:- boys age=18
and his brother age=7