0=8/x^3-2x

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Solution for 0=8/x^3-2x equation: 


D( x )

x^3 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

x in (-oo:0) U (0:+oo)

0 = 8/(x^3)-(2*x) // - 8/(x^3)-(2*x)

2*x-(8/(x^3))+0 = 0

2*x-8*x^-3 = 0

2*x-8*x^-3 = 0

2*x*(1-4*x^-4) = 0

-4*x^-4 = -1 // : -4

x^-4 = 1/4

-4 < 0

1/(x^4) = 1/4 // * x^4

1 = 1/4*x^4 // : 1/4

4 = x^4

x^4 = 4 // ^ 1/4

abs(x) = 4^(1/4)

x = 4^(1/4) or x = -4^(1/4)

2*x = 0

2*x = 0 // : 2

x = 0

x in { 0} 

x in { 4^(1/4), -4^(1/4) }

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