Question

Select the correct answer from each drop-down menu.Consider this equation.(47)}- I = 0The first step in solving this equation is toSolving this equation for x initially yleldsThe second step is toChecking the solutions shows thatResetNextentum. All rights reserved.A

Answer 1

Given:

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

To solve for x:

The first step in solving the equation is to add x on both sides, we get

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

The second step in solving the equation is to take the cube on both sides we get,

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

Solving this equation for x initially yields three possible values.

`\begin{gathered} x(x^2-4)=0\Rightarrow x=0^{} \\ Since,x^2=4 \\ \Rightarrow x=\pm2 \end{gathered}`

Hence, 0, -2, and 2 are the valid solutions.