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

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Solution for 1/4(x^3-1/x^3) 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)

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

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

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

x^3-x^-3 = 0

x^-3*(x^6-1) = 0

1*x^6 = 1 // : 1

x^6 = 1

x^6 = 1 // ^ 1/6

abs(x) = 1

x = 1 or x = -1

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

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

( 1/4 )

1/4 = 0

x belongs to the empty set

( x+1 )

x+1 = 0 // - 1

x = -1

( x-1 )

x-1 = 0 // + 1

x = 1

( x^-3 )

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

x^-3 = 0

x należy do O

x in { -1, 1 }

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