Question

I need the correct answer i have 1 more chance at the question and i must complete 100% mastery to get credit for my homework

Answer 1

Given:

The equation is

`2x^{(5)/(3)}-18x=0`

Required:

Find the non-zero solution to the equation.

Step-by-step explanation:

The given equation is

`2x^{(5)/(3)}-18x=0`

Rewrite the equation as:

`2x^{(5)/(3)}=18x`

Divide both sides by 2.

`x^{(5)/(3)}=9x`

Take cube on both sides.

`\begin{gathered} (x^{(5)/(3)})^3=(9x)^3 \\ x^5=729x^3 \\ x^5-729x^3=0 \end{gathered}`

Take out common x

`x^3`
`x^3(x^2-729)=0`

Find the factor by using the formula

`a^2-b^2=(a-b)(a+b)`
`\begin{gathered} x^3(x-27)(x+27)=0 \\ x=0,27,-27 \end{gathered}`

Final Answer:

Thus the non-zero solutions to the given equation are x =27, -27.