(1/x^3)+(8/x^2)+(16/x)=0

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Solution for (1/x^3)+(8/x^2)+(16/x)=0 equation:


D( x )

x^3 = 0

x = 0

x^2 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

x = 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)

16/x+8/(x^2)+1/(x^3) = 0

16*x^-1+8*x^-2+x^-3 = 0

t_1 = x^-1

1*t_1^3+8*t_1^2+16*t_1^1 = 0

t_1^3+8*t_1^2+16*t_1 = 0

t_1*(t_1^2+8*t_1+16) = 0

t_1^2+8*t_1+16 = 0

DELTA = 8^2-(1*4*16)

DELTA = 0

t_1 = -8/(1*2)

t_1 = -4 or t_1 = -4

t_1 = 0

t_1 = 0

t_1 = -4

x^-1+4 = 0

1*x^-1 = -4 // : 1

x^-1 = -4

-1 < 0

1/(x^1) = -4 // * x^1

1 = -4*x^1 // : -4

-1/4 = x^1

x = -1/4

t_1 = -4

x^-1+4 = 0

1*x^-1 = -4 // : 1

x^-1 = -4

-1 < 0

1/(x^1) = -4 // * x^1

1 = -4*x^1 // : -4

-1/4 = x^1

x = -1/4

t_1 = 0

x^-1+0 = 0

x^-1 = 0

1*x^-1 = 0 // : 1

x^-1 = 0

x naleu017Cy do O

x in { -1/4, -1/4 }

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