Question

the age of a man 9 years after he is square of the age 33 years ago find the present age of the man

Answer 1

Let the present age = x

the age of a man 9 years after he is square of the age 33 years ago

$x + 9 = {(x - 33)}^{2} \\ \\ {x}^{2} - 66x + 1089 = x + 9 \\ \\ {x}^{2} - 66x + 1089 - x - 9 = 0 \\ \\ {x}^{2} - 67x + 1080 = 0 \\ \\ {x}^{2} - 40x - 27x - 1080 = 0 \\ \\ x(x - 40) - 27(x - 40) = 0 \\ \\ (x - 40)(x - 27) = 0 \\ \\ x = 27 \: \: and \: \: 40$

But if he is 27 years old, he won't be born before 33 years. So he can't be 27 years old.

So he is 40 years old.