8X-1/X^2=0

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Solution for 8X-1/X^2=0 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)) = 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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