Question

What is the solution set of x

Answer 1

The solution to x is 6

Answer 2

Choices D is the correct answer.

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.