Answer:
Choices D is the correct answer.
Step-by-step explanation:
We have given an equation.
[tex]x^{2/3} -x^{1/3} +4 = 6[/tex]
We have to find solution of given equation.
Let [tex]x^{1/3} = y[/tex]
then, [tex]x^{2/3} = y^{2}[/tex]
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
[tex]x^{1/3} = 2[/tex] or [tex]x^{1/3} = -1[/tex]
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.
