x^4-2x^2-3/x^4+2x^2+1

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Solution for x^4-2x^2-3/x^4+2x^2+1 equation: 


D( x )

x^4 = 0

x^4 = 0

x^4 = 0

1*x^4 = 0 // : 1

x^4 = 0

x = 0

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

x^4-(2*x^2)+2*x^2-(3/(x^4))+1 = 0

x^4-2*x^2+2*x^2-3*x^-4+1 = 0

x^4-3*x^-4+1 = 0

t_1 = x^4

1*t_1^1-3*t_1^-1+1 = 0

1*t_1^1-3*t_1^-1+1*t_1^0 = 0

(1*t_1^2+1*t_1^1-3*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2+1*t_1^1-3*t_1^0) = 0

t_1^1

t_1^2+t_1-3 = 0

t_1^2+t_1-3 = 0

DELTA = 1^2-(-3*1*4)

DELTA = 13

DELTA > 0

t_1 = (13^(1/2)-1)/(1*2) or t_1 = (-13^(1/2)-1)/(1*2)

t_1 = (13^(1/2)-1)/2 or t_1 = (-(13^(1/2)+1))/2

t_1 in { (-(13^(1/2)+1))/2, (13^(1/2)-1)/2} 

t_1 = (-(13^(1/2)+1))/2

x^4-((-(13^(1/2)+1))/2) = 0

x^4+(1/2)*(13^(1/2)+1) = 0

1*x^4 = -(1/2*(13^(1/2)+1)) // : 1

x^4 = -1/2*(13^(1/2)+1)

t_1 = (13^(1/2)-1)/2

x^4-((13^(1/2)-1)/2) = 0

1*x^4 = (13^(1/2)-1)/2 // : 1

x^4 = (13^(1/2)-1)/2

x^4 = (13^(1/2)-1)/2 // ^ 1/4

abs(x) = ((13^(1/2)-1)^(1/4))/(2^(1/4))

x = ((13^(1/2)-1)^(1/4))/(2^(1/4)) or x = -(((13^(1/2)-1)^(1/4))/(2^(1/4)))

x in { ((13^(1/2)-1)^(1/4))/(2^(1/4)), -(((13^(1/2)-1)^(1/4))/(2^(1/4))) }

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