(x^1/3-1/4x^-1/3)^2

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Solution for (x^1/3-1/4x^-1/3)^2 equation: 


D( x )

x = 0

x = 0

x = 0

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

((x^1)/3-(((1/4)*x^-1)/3))^2 = 0

(x/3+(-1/12)*x^-1)^2 = 0

(1/3*x-1/12*x^-1)^2 = 0

1/3*x-1/12*x^-1 = 0

1/3*x^-1*(x^2-1/4) = 0

1*x^2 = 1/4 // : 1

x^2 = 1/4

x^2 = 1/4 // ^ 1/2

abs(x) = 1/2

x = 1/2 or x = -1/2

1/3*x^-1*(x-1/2)*(x+1/2) = 0

(1/3*x^-1)^2*(x-1/2)^2*(x+1/2)^2 = 0

( 1/3*x^-1 )

1/3*x^-1 = 0 // : 1/3

x^-1 = 0

x należy do O

( x+1/2 )

x+1/2 = 0 // - 1/2

x = -1/2

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

x in { -1/2, -1/2, 1/2, 1/2 }

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