3/r=5/r3

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Solution for 3/r=5/r3 equation:


D( r )

r = 0

r^3 = 0

r = 0

r = 0

r^3 = 0

r^3 = 0

1*r^3 = 0 // : 1

r^3 = 0

r = 0

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

3/r = 5/(r^3) // - 5/(r^3)

3/r-(5/(r^3)) = 0

3/r-5*r^-3 = 0

3*r^-1-5*r^-3 = 0

t_1 = r^-1

3*t_1^1-5*t_1^3 = 0

3*t_1-5*t_1^3 = 0

t_1*(3-5*t_1^2) = 0

-5*t_1^2 = -3 // : -5

t_1^2 = 3/5

t_1^2 = 3/5 // ^ 1/2

abs(t_1) = (3/5)^(1/2)

t_1 = (3/5)^(1/2) or t_1 = -(3/5)^(1/2)

t_1 = 0

t_1 = 0

t_1 = (3/5)^(1/2)

r^-1-(3/5)^(1/2) = 0

1*r^-1 = (3/5)^(1/2) // : 1

r^-1 = (3/5)^(1/2)

-1 < 0

1/(r^1) = (3/5)^(1/2) // * r^1

1 = (3/5)^(1/2)*r^1 // : (3/5)^(1/2)

1/((3/5)^(1/2)) = r^1

r = 1/((3/5)^(1/2))

t_1 = -(3/5)^(1/2)

r^-1+(3/5)^(1/2) = 0

1*r^-1 = -(3/5)^(1/2) // : 1

r^-1 = -(3/5)^(1/2)

-1 < 0

1/(r^1) = -(3/5)^(1/2) // * r^1

1 = -(3/5)^(1/2)*r^1 // : -(3/5)^(1/2)

1/(-(3/5)^(1/2)) = r^1

r = 1/(-(3/5)^(1/2))

t_1 = 0

r^-1+0 = 0

r^-1 = 0

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

r^-1 = 0

r należy do O

r in { 1/((3/5)^(1/2)), 1/(-(3/5)^(1/2)) }

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