(2x^2+1/x-1)^5

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


D( x )

x = 0

x = 0

x = 0

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

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

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

2*x^2+x^-1-1 = 0

2*x^2+1*x^-1-1*x^0 = 0

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

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

x^1

2*x^3-x+1 = 0

{ 1, -1 }

1

x = 1

2*x^3-x+1 = 2

1

-1

x = -1

2*x^3-x+1 = 0

-1

x+1

2*x^2-2*x+1

2*x^3-x+1

x+1

-2*x^3-2*x^2

1-2*x^2-x

2*x^2+2*x

x+1

-x-1

0

2*x^2-2*x+1 = 0

DELTA = (-2)^2-(1*2*4)

DELTA = -4

DELTA < 0

x in { -1} 

x+1 = 0

(x+1)^5 = 0

x+1 = 0 // - 1

x = -1

x in { -1, -1, -1, -1, -1 }

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