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# Solve for x

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Hi good people!,

Please help me out here...Solve for x in the equation:

$$x^{1 \over3}=4{1 \over x^3}$$

what I did was raise everything to another power of 3,

$$x=64{1 \over x^9}$$,

then multiplied by $$x^9$$

$$x^{10}=64$$,

then I'm stuck...

Apr 29, 2018

### 10+0 Answers

#1
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Here is my solution.

$$x^\frac{1}{3} = y$$

y = 4 / y

y^2 = 4

y = 2

$$x^\frac{1}{3}=2$$

x = the cube root of 2

I hope this helped,

Gavin

Apr 29, 2018
#2
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Never mind, I though the denominator was $$x^\frac{1}{3}$$

My answer is wrong.

Apr 29, 2018
#7
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GYanggg,

thank you for trying...I do appreciate..

juriemagic  Apr 30, 2018
#3
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Solve for x:
x^(1/3) = 4/x^3

Raise both sides to the power of three:
x = 64/x^9

Cross multiply:
x^10 = 64        Take the 10th root of both sides
x = 2^(3/5)      or        x= (-2)^(3/5)

These 2 solutions are the only real solution to balance the equation.

Apr 29, 2018
edited by Guest  Apr 29, 2018
#5
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x^{1 \over3}=4{1 \over x^3}

$$x^{1 \over3}=4{1 \over x^3}\\ x^{1 \over3}=4x^{-3}\\ x=4^3*x^{-9}\\ x^{10}=4^3\\ x=4^{3/10}\\ x=2^{3/5}\\ x=\sqrt{8}\\ x\approx 1.5157$$

this is the only positive real answer.

I think our guest's negative answer also works.  It may not work with convention though

The cube root is in the question. so is a negative allowed.. I am not sure.

I think there are other complex answers as well.

.
Apr 30, 2018
edited by Melody  Apr 30, 2018
edited by Melody  Apr 30, 2018
#8
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Hi Melody,

a Million thank you's...I think your answer is closest to what I believe the answer should be. I do appreciate!

juriemagic  Apr 30, 2018
#6
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One more try:

a$$x^{\frac{1}{3}}=4{\frac{1}{x^3}}$$

definition:

$${\color{black}is}\ 4\frac{1}{3}=4 +\frac{1}{3}\ {\color{black}so\ is}\ 4\frac{1}{x^3}=4 +\frac{1}{x^3}$$

$$x^{\frac{1}{3}}=4+{\frac{1}{x^3}}$$         |  $$\times x^3$$

$$x^{\frac{10}{3}}=4x^3+1$$

$$f(x)=4x^3-x^{\frac{10}{3}}+1 \neq 0$$

The function has a minimum in P (0;1).
The function has no zero. !

Apr 30, 2018
edited by asinus  Apr 30, 2018
#9
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asinus,

wow, this is something else!!..would never have thought of going that route. I do appreciate your help! Thank you..

juriemagic  Apr 30, 2018
#12
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If you smoke some whackyweed you might think of going that route.

Asinus is a natural space cadet, so he probably doesn’t need to smoke any.

Maybe it would help, if he did.

Guest May 1, 2018