Question

consider this equation. (4x)^1\3-x=0. the first be step in solving this equation is to _____. the second step is to ______. solving this equation for x initially yields_____. checking the solutions shows that_____.

Answer 1

Given equation

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

The first step in solving the equation is to remove the roots

Multiply the equation by the power 3 on both side

`(4x^{(1)/(3)})^3=x^3`
`64x=x^3`

Now divide the equation with x

`\begin{gathered} (64x)/(x)=(x^3)/(x) \\ 64=x^2 \end{gathered}`

Now, taking the square root on the both side of the equation

`\sqrt[]{64}=\sqrt[]{x^2}`
`x=\pm8,0`

the value of x=(-8), 8, 0.

ANSWER:

The first step in solving this equation is cubing the equation.

The second stepp in solving the equation is divide equation with x and taking square root.

For, (-2,2,0)

Put x=(-2)

`\begin{gathered} 4x^{(1)/(3)}-x=0 \\ 4(-2)^{(1)/(3)}-(-2) \\ 4(-1.259)+2 \\ -5.036+2 \\ -3.036\\e0 \end{gathered}`

So, x=(-2) is note the solution of the given equation