2x^-1/3(x^5/3-4x^1/3)

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Solution for 2x^-1/3(x^5/3-4x^1/3) equation:


D( x )

x = 0

x = 0

x = 0

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

((2*x^-1)/3)*((x^5)/3-((4*x^1)/3)) = 0

((2*x^-1)/3)*((x^5)/3+(-4/3)*x) = 0

2/3*x^-1*(1/3*x^5-4/3*x) = 0

1/3*x^5-4/3*x = 0

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

1*x^4 = 4 // : 1

x^4 = 4

x^4 = 4 // ^ 1/4

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

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

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

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

( 1/3*x )

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

x = 0

( 2/3*x^-1 )

2/3*x^-1 = 0 // : 2/3

x^-1 = 0

x należy do O

( x+4^(1/4) )

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

x = -4^(1/4)

( x-4^(1/4) )

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

x = 4^(1/4)

x in { 0}

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

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