1/k^5=8/k^2

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Solution for 1/k^5=8/k^2 equation: 


D( k )

k^2 = 0

k^5 = 0

k^2 = 0

k^2 = 0

1*k^2 = 0 // : 1

k^2 = 0

k = 0

k^5 = 0

k^5 = 0

1*k^5 = 0 // : 1

k^5 = 0

k = 0

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

1/(k^5) = 8/(k^2) // - 8/(k^2)

1/(k^5)-(8/(k^2)) = 0

1/(k^5)-8*k^-2 = 0

1*k^-5-8*k^-2 = 0

(1*k^0-8*k^3)/(k^5) = 0 // * k^10

k^5*(1*k^0-8*k^3) = 0

k^5

1-8*k^3 = 0

{ 1, -1 }

1

k = 1

1-8*k^3 = -7

1

-1

k = -1

1-8*k^3 = 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

k

1/2

1-8*k^3 = 0

1/2

k-1/2

-8*k^2-4*k-2

1-8*k^3

k-1/2

8*k^3-4*k^2

1-4*k^2

4*k^2-2*k

1-2*k

2*k-1

0

-8*k^2-4*k-2 = 0

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

DELTA = -48

DELTA < 0

k in { 1/2} 

k = 1/2

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