Question

What is the solution set of x for the given equation? x^(2/3)-x^(1/3)+4=6

Answer 1

(8,-1)

Explanation:

Answer 2

`\bf x^{(2)/(3)}-x^{(1)/(3)}+4=6\implies x^{(2)/(3)}-x^{(1)/(3)}-2=0 \\\\\\ \left( x^{(1)/(3)} \right)^2-\left( x^{(1)/(3)} \right)-2=0\impliedby \textit{now, that's just a quadratic}`


`\bf \left( x^{(1)/(3)}-2 \right)\left( x^{(1)/(3)}+1 \right)=0\implies \begin{cases} x^{(1)/(3)}-2=0\\ x^{(1)/(3)}=2\\ \left( x^{(1)/(3)} \right)^3=2^3\\\\ \boxed{x=8}\\ ----------\\ x^{(1)/(3)}+1=0\\ x^{(1)/(3)}=-1\\ \left( x^{(1)/(3)} \right)^3=(-1)^3\\\\ \boxed{x=-1} \end{cases}`