x^2-4=2/x^2

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Solution for x^2-4=2/x^2 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^2-4 = 2/(x^2) // - 2/(x^2)

x^2-(2/(x^2))-4 = 0

x^2-2*x^-2-4 = 0

t_1 = x^2

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

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

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

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

t_1^1

t_1^2-4*t_1-2 = 0

t_1^2-4*t_1-2 = 0

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

DELTA = 24

DELTA > 0

t_1 = (24^(1/2)+4)/(1*2) or t_1 = (4-24^(1/2))/(1*2)

t_1 = (2*6^(1/2)+4)/2 or t_1 = (4-2*6^(1/2))/2

t_1 in { (4-2*6^(1/2))/2, (2*6^(1/2)+4)/2} 

t_1 = (4-2*6^(1/2))/2

x^2-((4-2*6^(1/2))/2) = 0

1*x^2 = (4-2*6^(1/2))/2 // : 1

x^2 = (4-2*6^(1/2))/2

t_1 = (2*6^(1/2)+4)/2

x^2-((2*6^(1/2)+4)/2) = 0

1*x^2 = (2*6^(1/2)+4)/2 // : 1

x^2 = (2*6^(1/2)+4)/2

x^2 = (2*6^(1/2)+4)/2 // ^ 1/2

abs(x) = ((2*6^(1/2)+4)^(1/2))/(2^(1/2))

x = ((2*6^(1/2)+4)^(1/2))/(2^(1/2)) or x = -(((2*6^(1/2)+4)^(1/2))/(2^(1/2)))

x in { ((2*6^(1/2)+4)^(1/2))/(2^(1/2)), -(((2*6^(1/2)+4)^(1/2))/(2^(1/2))) }

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