0.25=(2.75/r)^12-(2.75/r)^6

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Solution for 0.25=(2.75/r)^12-(2.75/r)^6 equation: 


D( r )

r = 0

r = 0

r = 0

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

0.25 = (2.75/r)^12-(2.75/r)^6 // - (2.75/r)^12-(2.75/r)^6

(2.75/r)^6-(2.75/r)^12+0.25 = 0

2.75^6*r^-6-r^-12+0.25 = 0

t_1 = r^-6

2.75^6*t_1^1-1*t_1^2+0.25 = 0

2.75^6*t_1-t_1^2+0.25 = 0

DELTA = (2.75^6)^2-(-1*0.25*4)

DELTA = 2.75^12+1

DELTA = 187065.90854746

DELTA > 0

t_1 = ((2.75^12+1)^(1/2)-2.75^6)/(-1*2) or t_1 = (-2.75^6-(2.75^12+1)^(1/2))/(-1*2)

t_1 = ((2.75^12+1)^(1/2)-2.75^6)/(-2) or t_1 = (2.75^6+(2.75^12+1)^(1/2))/2

t_1 = ((2.75^12+1)^(1/2)-2.75^6)/(-2)

r^-6-(((2.75^12+1)^(1/2)-2.75^6)/(-2)) = 0

1*r^-6 = ((2.75^12+1)^(1/2)-2.75^6)/(-2) // : 1

r^-6 = ((2.75^12+1)^(1/2)-2.75^6)/(-2)

-6 < 0

1/(r^6) = ((2.75^12+1)^(1/2)-2.75^6)/(-2) // * r^6

1 = (((2.75^12+1)^(1/2)-2.75^6)/(-2))*r^6 // : ((2.75^12+1)^(1/2)-2.75^6)/(-2)

-2*((2.75^12+1)^(1/2)-2.75^6)^-1 = r^6

t_1 = (2.75^6+(2.75^12+1)^(1/2))/2

r^-6-((2.75^6+(2.75^12+1)^(1/2))/2) = 0

1*r^-6 = (2.75^6+(2.75^12+1)^(1/2))/2 // : 1

r^-6 = (2.75^6+(2.75^12+1)^(1/2))/2

-6 < 0

1/(r^6) = (2.75^6+(2.75^12+1)^(1/2))/2 // * r^6

1 = ((2.75^6+(2.75^12+1)^(1/2))/2)*r^6 // : (2.75^6+(2.75^12+1)^(1/2))/2

2*(2.75^6+(2.75^12+1)^(1/2))^-1 = r^6

r^6 = 2*(2.75^6+(2.75^12+1)^(1/2))^-1 // ^ 1/6

abs(r) = 2^(1/6)*(2.75^6+(2.75^12+1)^(1/2))^(-1/6)

r = 2^(1/6)*(2.75^6+(2.75^12+1)^(1/2))^(-1/6) or r = -(2^(1/6)*(2.75^6+(2.75^12+1)^(1/2))^(-1/6))

r in { 2^(1/6)*(2.75^6+(2.75^12+1)^(1/2))^(-1/6), -(2^(1/6)*(2.75^6+(2.75^12+1)^(1/2))^(-1/6)) }

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