0=x^1/2-32x^-2

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Solution for 0=x^1/2-32x^-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

0 = (x^1)/2-(32*x^-2) // - (x^1)/2-(32*x^-2)

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

32*x^-2-(x/2) = 0

32*x^-2-1/2*x^1 = 0

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

x^2*(32*x^0-1/2*x^3) = 0

x^2

(-1/2)*x^3+32 = 0

(-1/2)*x^3+32 = 0 // * 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }

1

x = 1

64-x^3 = 63

1

-1

x = -1

64-x^3 = 65

-1

2

x = 2

64-x^3 = 56

2

-2

x = -2

64-x^3 = 72

-2

4

x = 4

64-x^3 = 0

4

x-4

-x^2-4*x-16

64-x^3

x-4

x^3-4*x^2

64-4*x^2

4*x^2-16*x

64-16*x

16*x-64

0

-x^2-4*x-16 = 0

DELTA = (-4)^2-(-16*(-1)*4)

DELTA = -48

DELTA < 0

x in { 4} 

x = 4

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