Question

. 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 replied the boy. What was his age.​

Answer 1

Answer:

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

Answer 2

Given,

Add the square root of age to half of the age.

Then subtract 12.

To Find,

The boy's age.

Solution,

Let's take the boy's age = y.

The square root of age + half of age

$\sqrt{y}$ + y /2  

Then 12 is subtracted from the above.

$\sqrt{y}$ + y/2 - 12

And the boy said the result of the above equation is nothing.

That is,

$\sqrt{y}$ + y/2 -12 = 0    

Let's take a substitute for $\sqrt{y}$ = a.

a + $a^{2}$/2 -12 = 0

$a^{2}$ + 2a - 24 = 0

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

Therefore,

a = -6, 4.

and a = $\sqrt{y}$

y = $a^{2}$

y = 36,16.

Hence, 16is the age of the boy.