5/x=20/x13

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Solution for 5/x=20/x13 equation: 


D( x )

x = 0

x^13 = 0

x = 0

x = 0

x^13 = 0

x^13 = 0

1*x^13 = 0 // : 1

x^13 = 0

x = 0

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

5/x = 20/(x^13) // - 20/(x^13)

5/x-(20/(x^13)) = 0

5/x-20*x^-13 = 0

5*x^-1-20*x^-13 = 0

t_1 = x^-1

5*t_1^1-20*t_1^13 = 0

5*t_1-20*t_1^13 = 0

5*t_1*(1-4*t_1^12) = 0

-4*t_1^12 = -1 // : -4

t_1^12 = 1/4

t_1^12 = 1/4 // ^ 1/12

abs(t_1) = (1/4)^(1/12)

t_1 = (1/4)^(1/12) or t_1 = -(1/4)^(1/12)

5*t_1 = 0

5*t_1 = 0 // : 5

t_1 = 0

t_1 = (1/4)^(1/12)

x^-1-(1/4)^(1/12) = 0

1*x^-1 = (1/4)^(1/12) // : 1

x^-1 = (1/4)^(1/12)

-1 < 0

1/(x^1) = (1/4)^(1/12) // * x^1

1 = (1/4)^(1/12)*x^1 // : (1/4)^(1/12)

1/((1/4)^(1/12)) = x^1

x = 1/((1/4)^(1/12))

t_1 = -(1/4)^(1/12)

x^-1+(1/4)^(1/12) = 0

1*x^-1 = -(1/4)^(1/12) // : 1

x^-1 = -(1/4)^(1/12)

-1 < 0

1/(x^1) = -(1/4)^(1/12) // * x^1

1 = -(1/4)^(1/12)*x^1 // : -(1/4)^(1/12)

1/(-(1/4)^(1/12)) = x^1

x = 1/(-(1/4)^(1/12))

t_1 = 0

x^-1+0 = 0

x^-1 = 0

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

x^-1 = 0

x należy do O

x in { 1/((1/4)^(1/12)), 1/(-(1/4)^(1/12)) }

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