Question

the sum of the age of the father and his son is 42 years the product of their age is 185 find the range​

Answer 1

Let age of son be x and father be y.
So, According to question
x + y = 42
x = 42 - y
And
xy = 185
(42 - y)y = 185
$42y - {y}^{2} = 185$
$42y - {y}^{2} - 185 = 0$
$- {y}^{2} + 42y - 185 = 0$
${y}^{2} - 42y + 185 = 0$
(Taking -1 as common and transporting it to 0 and dividing with 0 resulting to 0 only in RHS)

Now , By Spilting the middle term method

${y}^{2} - 37y - 5y + 185 = 0$
$y(y - 37) - 5(y - 37) = 0$
$(y - 37)(y - 5) = 0$
$y = 5 or 37$
So value of y is 5 or 37 , But As father is always elder than son so y is 37.
x = 42 - 37 = 5
So, Father's age is 37 years and son's age is 5 years