That Root is Radical!

You just change the root to expoential number. After that, its easy to evaluate this!

1. Change the root to exponent, like this. Note : symbol of ^ is the exponent 2^12/X = 2^2 x 2^1/2(X+1) because general number already same, is 2, so, eliminate the number. like this : 12/X = 2 x (1/2 (X+1)) 12/X = 2 x (1/2X + 1/2) 12/X = X + 1 12 = X^2 + X so, it become X^2 + X -12, use factorization to solve this. (X+4) (X-3) or X = -4 and X= 3. because brilliant only admit the answer fron 0-999, it certainly 3 as an answer.

Let's start... Slightly rewriting, we get...

$2^{\frac {12}{x}}=2^{2} \times 2^{\frac {x+1}{2}} \Longrightarrow 2^{\frac {12}{x}}=2^{\frac {x+5}{2}}$

$\Longrightarrow \frac {12}{x}= \frac {x+5}{2} \Longrightarrow x^2+5x-24=0 \Longrightarrow (x-3)(x+8)=0$

Hence, the only positive integer solution to $x$ is $\fbox {3}$

2^12/x= 2^2+ 2^1/2.x+1/2 12/x= 5/2+1/2.x 12/x-1/2.x=5/2 -x²-5x+24=0 faz baskara e da -8 e 3, como pede o inteiro positivo, fica o 3!

3

(x root of 2) ^ 12 = (2 ^ 2) * (squareroot of 2) ^ (x + 1):> I change the radical to an exponent to make managing the equation easier.:> 2 ^ (12 / x) = 4 * (squareroot of 2) ^ (x + 1):> Since 4 is (the squareroot of 2) ^ 4, and is being multiplied to a like term of (squareroot of 2) ^ (x + 1), I can add the exponents together to get::> 2 ^ (12 / x) = (squareroot of 2) ^ (x + 5).:> to make the terms the same on each side of the equation, I can convert the [2 ^ (12 / x)] to [(Squareroot of 2) ^ (24 / x)].:> (Squareroot of 2) ^ (24 / x) = (squareroot of 2) ^ (x + 5):> I knoticed that when x = 3, 3 + 5 = 8 and 8 * 3 = 24.:> (Squareroot of 2) ^ (24 / 3) = (squareroot of 2) ^ (3 + 5):> (Squareroot of 2) ^ (8) = (squareroot of 2) ^ (8):> 2 ^ 4 = 2 ^ 4:> 16 = 16:> x = 3:> solved

compare the power of both sides 12/x =2+((x+1)/2) then solve equation for x and get answer

1 + 2 =3

2^(12/x)=2^2 (2^(x+1)/2) 2^(12/x)=2^(2+(x+1)/2) 2^(12/x)=2^((5+x)/2) 12/x=(5+x)/2 X^2+5 x-24=0 (x+8)(x-3)=0 x= -8 or x=3 hence positive integer of x=3