-4/x^2-16+x/2x+8

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Solution for -4/x^2-16+x/2x+8 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(x/2)*x-4/(x^2)-16+8 = 0

1/2*x^2-4*x^-2-8 = 0

t_1 = x^2

1/2*t_1^1-4*t_1^-1-8 = 0

1/2*t_1^1-4*t_1^-1-8*t_1^0 = 0

(1/2*t_1^2-8*t_1^1-4*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1/2*t_1^2-8*t_1^1-4*t_1^0) = 0

t_1^1

(1/2)*t_1^2-8*t_1-4 = 0

(1/2)*t_1^2-8*t_1-4 = 0

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

DELTA = 72

DELTA > 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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