1/x^2=27/x^5

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Solution for 1/x^2=27/x^5 equation: 


D( x )

x^5 = 0

x^2 = 0

x^5 = 0

x^5 = 0

1*x^5 = 0 // : 1

x^5 = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1/(x^2) = 27/(x^5) // - 27/(x^5)

1/(x^2)-(27/(x^5)) = 0

1/(x^2)-27*x^-5 = 0

1*x^-2-27*x^-5 = 0

(1*x^3-27*x^0)/(x^5) = 0 // * x^10

x^5*(1*x^3-27*x^0) = 0

x^5

x^3-27 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27 }

1

x = 1

x^3-27 = -26

1

-1

x = -1

x^3-27 = -28

-1

3

x = 3

x^3-27 = 0

3

x-3

x^2+3*x+9

x^3-27

x-3

3*x^2-x^3

3*x^2-27

9*x-3*x^2

9*x-27

27-9*x

0

x^2+3*x+9 = 0

DELTA = 3^2-(1*4*9)

DELTA = -27

DELTA < 0

x in { 3} 

x = 3

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