x^2-4/x^2-1

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Solution for x^2-4/x^2-1 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/(x^2))-1 = 0

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

t_1 = x^2

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

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

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

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

t_1^1

t_1^2-t_1-4 = 0

t_1^2-t_1-4 = 0

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

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)+1)/(1*2) or t_1 = (1-17^(1/2))/(1*2)

t_1 = (17^(1/2)+1)/2 or t_1 = (1-17^(1/2))/2

t_1 in { (1-17^(1/2))/2, (17^(1/2)+1)/2} 

t_1 = (1-17^(1/2))/2

x^2-((1-17^(1/2))/2) = 0

1*x^2 = (1-17^(1/2))/2 // : 1

x^2 = (1-17^(1/2))/2

t_1 = (17^(1/2)+1)/2

x^2-((17^(1/2)+1)/2) = 0

1*x^2 = (17^(1/2)+1)/2 // : 1

x^2 = (17^(1/2)+1)/2

x^2 = (17^(1/2)+1)/2 // ^ 1/2

abs(x) = ((17^(1/2)+1)^(1/2))/(2^(1/2))

x = ((17^(1/2)+1)^(1/2))/(2^(1/2)) or x = -(((17^(1/2)+1)^(1/2))/(2^(1/2)))

x in { ((17^(1/2)+1)^(1/2))/(2^(1/2)), -(((17^(1/2)+1)^(1/2))/(2^(1/2))) }

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