Question

Select the correct answer from each drop-down menu.Consider this equation.First Step is to 1. take the cube root of both sides. 2. Add x to both sides. 3. cube both sidesSecond Step is 1. Add the cube root of X to both sides. 2. Cube both sides. 3. Add the cube of x to both sidesSolving this equation for x initially yields 1. Two possible Solutions. 2. One possible solution. 3. Three possible solutionsChecking the Solutions show that. 1. 0 and 2 are valid solutions. 2. only 0 is valid. 3. -2,0, and 2 are valid solutions. 4. None are valid

Answer 1

First step is to add x to both sides.

Second step is cube both sides.

Solving this equation for x initially yields three possible solutions.

`\begin{gathered} (4x)^{(1)/(3)}-x=0 \\ (4x)^{(1)/(3)}=x \\ 4x=x^3 \\ x^3-4x=0 \\ x(x^2-4)=0 \\ then_{} \\ x=0 \\ or \\ x^2-4=0 \\ x^2=4 \\ x=\pm2 \end{gathered}`

Checking the solutions show that -2, 0 and 2 are valid solutions.