8x=1/x^2

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Solution for 8x=1/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

8*x = 1/(x^2) // - 1/(x^2)

8*x-(1/(x^2)) = 0

8*x-x^-2 = 0

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

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

x^2*(8*x^3-1*x^0) = 0

x^2

8*x^3-1 = 0

{ 1, -1 }

1

x = 1

8*x^3-1 = 7

1

-1

x = -1

8*x^3-1 = -9

-1

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8 }

1/2

x

1/2

8*x^3-1 = 0

1/2

x-1/2

8*x^2+4*x+2

8*x^3-1

x-1/2

4*x^2-8*x^3

4*x^2-1

2*x-4*x^2

2*x-1

1-2*x

0

8*x^2+4*x+2 = 0

DELTA = 4^2-(2*4*8)

DELTA = -48

DELTA < 0

x in { 1/2} 

x = 1/2

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