Question

Select the correct answer from each drop-down menu. Consider this equation 0 . The first step in solving this equation is to Solving this equation for x initially yields The second step is to y. Checking the solutions shows that

Answer 1

The given equation is

`(4x)^{(1)/(3)}-x=0`

The first step, add x to both sides

`\begin{gathered} (4x)^{(1)/(3)}-x+x=0+x \\ (4x)^{(1)/(3)}=x \end{gathered}`

Cube each side ------ 2nd answer

`\begin{gathered} (4x)^{(1)/(3)*3}=x^(1*3) \\ 4x=x^3 \end{gathered}`

Now, Subtract 4x from both sides

`\begin{gathered} 4x-4x=x^3-4x \\ 0=x^3-4x \\ x^3-4x=0 \end{gathered}`

Take x as a common

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

Equate x by 0 and x^2 - 4 by 0 to find the values of x

`\begin{gathered} x=0 \\ x^2-4=0 \\ x^2-4+4=0+4 \\ x^2=4 \\ \sqrt[]{x^2}=\pm\sqrt[]{4} \\ x=\pm2 \end{gathered}`

The values of x are 0, 2, -2

Let us check them

`(4*0)^{(1)/(3)}-0=0-0=0\rightarrow True`
`(4*-2)^{(1)/(3)}-(-2)=(-8)^{(1)/(3)}+2=-2+2=0\rightarrow True`
`(4*2)^{(1)/(3)}-(2)=(8)^{(1)/(3)}-2=2-2=0\rightarrow True`

The equation has 3 possible solutions ----- 3rd answer

The last answer is -2, 0, 2 ------- 1st answer