How do I solve and what is the answer?

Question

Solve: k^(2/3)-3k^(1/3)=4 

Answer 1

Use the substitutions   

 

x = k^1/3

 

x² = (k^1/3)² = k^2/3

 

 

Therefore, we have

 

x² - 3x = 4

 

x² - 3x - 4 = 0

 

(x - 4)(x + 1) = 0

 

x = 4           and          x = -1

 

 

Substitute these values of x into k.

 

x³ = k

 

4³ = k             and             (-1)³ = k

 

 

Solve for the two values of k.  Then verify the values of k by plugging them into the original equation.