if 3�ãx6 + 3�ã8x3 + 3�ã1 = 0, then x=
(A) -1
(B) 0
(C) 1
(D) 2
(E) 3
To solve the equation 3√(x*6) + 3√(8x*3) + 3√(1) = 0, we need to isolate the variable x. Let's go step by step:
Step 1: Simplify the equation
Rewriting the cube roots in exponential form, the equation becomes:
3(x^2) + 3(2x) + 3 = 0
Step 2: Combine like terms
Simplifying further, we have:
3x^2 + 6x + 3 = 0
Step 3: Divide the entire equation by 3 to simplify it
Dividing by 3, we get:
x^2 + 2x + 1 = 0
Step 4: Factor the quadratic equation (x^2 + 2x + 1)
Factoring the quadratic equation, we find:
(x + 1)(x + 1) = 0
Step 5: Set each factor equal to zero
Setting both factors equal to zero, we have:
x + 1 = 0
Step 6: Solve for x
Solving for x, we get:
x = -1
Therefore, the answer is x = -1. So the correct choice is (A) -1.