Question

A boy was asked his age. 'If you add the square of it to half of it and then subtract $12$, the answer will be nothing" replied the boy. What was his age?

Answer 1

Let $x$ be the age of a boy

$\sqrt{x}+\frac{x}{2}-12=0$

let $u=\sqrt{x}$

Now,

$u+\frac{u^2}{2}-12=0$

$u^2+2u-24=0$

$(u+6)(u-4)=0$

$u=-6$ or $u=4$

Now, $u=\sqrt{x}\Rightarrow x=u^2=36$ or $16$

Hence, his age is $16$