How would you solve the given equation?

Question

anonymous · Answer

.

mathstudent55 · Answer

Is the fraction 1/3 the exponent of x?

anonymous · Answer

Not sure, I honestly don't understand at all. here are the multiple choice answers if it helps? But I need the explanation on how to do it.

mathstudent55 · Answer

I don't understand how that problem can have those answers.

mathstudent55 · Answer

The equation looks like this to me.

$\Large x - 7x^{\frac{1}{3}} + 6 = 0$

anonymous · Answer

Yea same here but not, but I don't know what the "-" sign is suppose to be?

mathstudent55 · Answer

To solve this equation (assuming this is the correct equation), 
Move the exponent term to the right, and cube both sides.

mathstudent55 · Answer

$\Large x - 7x^{\frac{1}{3}} + 6 = 0$

$\Large x  + 6 =  7x^{\frac{1}{3}}$

$\Large (x  + 6)^3 =  (7x^{\frac{1}{3}})^3$

$\Large (x  + 6)^3 =  343x$

$\Large (x + 6)(x^2 + 12x + 36) = 343x$

$\Large x^3 + 12x^2 + 36x + 6x^2 + 72x + 216 = 343x$

$\Large x^3 + 18x^2 + 108x + 216 = 343x$

$\Large x^3 + 18x^2 - 235x + 216 = 0$

anonymous · Answer

$$7x ^{\frac{ 1 }{ 3 }} = x+6$$$$343x = x^3+18x^2+108x+216$$$$x^3+18x^2-235x+216=0$$But neither 216 nor -216 is a root.
Could there be something wrong with the question?

usukidoll · Answer

well plugging in x = 1 I do have the equation going to 0 .

usukidoll · Answer

maybe rational toot test might work?!

usukidoll · Answer

wow something is off with the question...

usukidoll · Answer

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