a^2-2a/a^3-8

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Solution for a^2-2a/a^3-8 equation: 


D( a )

a^3 = 0

a^3 = 0

a^3 = 0

1*a^3 = 0 // : 1

a^3 = 0

a = 0

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

a^2-((2*a)/(a^3))-8 = 0

a^2-2*a^-2-8 = 0

t_1 = a^2

1*t_1^1-2*t_1^-1-8 = 0

1*t_1^1-2*t_1^-1-8*t_1^0 = 0

(1*t_1^2-8*t_1^1-2*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-8*t_1^1-2*t_1^0) = 0

t_1^1

t_1^2-8*t_1-2 = 0

t_1^2-8*t_1-2 = 0

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

DELTA = 72

DELTA > 0

t_1 = (72^(1/2)+8)/(1*2) or t_1 = (8-72^(1/2))/(1*2)

t_1 = (6*2^(1/2)+8)/2 or t_1 = (8-6*2^(1/2))/2

t_1 in { (8-6*2^(1/2))/2, (6*2^(1/2)+8)/2} 

t_1 = (8-6*2^(1/2))/2

a^2-((8-6*2^(1/2))/2) = 0

1*a^2 = (8-6*2^(1/2))/2 // : 1

a^2 = (8-6*2^(1/2))/2

t_1 = (6*2^(1/2)+8)/2

a^2-((6*2^(1/2)+8)/2) = 0

1*a^2 = (6*2^(1/2)+8)/2 // : 1

a^2 = (6*2^(1/2)+8)/2

a^2 = (6*2^(1/2)+8)/2 // ^ 1/2

abs(a) = ((6*2^(1/2)+8)^(1/2))/(2^(1/2))

a = ((6*2^(1/2)+8)^(1/2))/(2^(1/2)) or a = -(((6*2^(1/2)+8)^(1/2))/(2^(1/2)))

a in { ((6*2^(1/2)+8)^(1/2))/(2^(1/2)), -(((6*2^(1/2)+8)^(1/2))/(2^(1/2))) }

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