a boy was asked his age: if you add the square root of it to half of it, and then subtract 12, the answer will be nothing, the boy replied. what was his age?

Question

quadratic equation, advanced algebra

Answer 1

x = age

 

√x + x/2 - 12 = 0

 

Substitution: u = √x

 

u + u²/2 - 12 = 0

 

u² + 2u - 24 = 0

 

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

 

u = -6 or 4

 

u = √x ⇒ x = u² = 36 or 16

 

Since he is a boy, pick 16 as the correct answer.