Question

What is the solution set of x

Answer 1

The solution to x is 6

Answer 2

Answer:

Choices D is the correct answer.

Step-by-step explanation:

We have given an equation.

$x^{2/3} -x^{1/3} +4 = 6$

We have to find solution of given equation.

Let $x^{1/3} = y$

then, $x^{2/3} = y^{2}$

Putting values in given equation, we have

y²-y+4 = 6

y²-y+4-6 = 0

y²-y-2 = 0

Applying factorization of above equation, we have

y²-2y+y-2 = 0

y(y-2)+1(y-2) = 0

(y-2)(y+1) = 0

Applying Zero-Product Property to above equation, we have

y-2 = 0 or y+1 = 0

y  = 2 or y = -1

$x^{1/3} = 2$  or $x^{1/3} = -1$

Taking cube on both sides of above equation, we have

x = (2)³ or x  = (-1)³

x  = 8 or x  = -1 which are the answer.