x^4+1/x^4-3

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Solution for x^4+1/x^4-3 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+1/(x^4)-3 = 0

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

t_1 = x^4

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

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

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

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

t_1^1

t_1^2-3*t_1+1 = 0

t_1^2-3*t_1+1 = 0

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

DELTA = 5

DELTA > 0

t_1 = (5^(1/2)+3)/(1*2) or t_1 = (3-5^(1/2))/(1*2)

t_1 = (5^(1/2)+3)/2 or t_1 = (3-5^(1/2))/2

t_1 in { (3-5^(1/2))/2, (5^(1/2)+3)/2} 

t_1 = (3-5^(1/2))/2

x^4-((3-5^(1/2))/2) = 0

1*x^4 = (3-5^(1/2))/2 // : 1

x^4 = (3-5^(1/2))/2

x^4 = (3-5^(1/2))/2 // ^ 1/4

abs(x) = ((3-5^(1/2))^(1/4))/(2^(1/4))

x = ((3-5^(1/2))^(1/4))/(2^(1/4)) or x = -(((3-5^(1/2))^(1/4))/(2^(1/4)))

t_1 = (5^(1/2)+3)/2

x^4-((5^(1/2)+3)/2) = 0

1*x^4 = (5^(1/2)+3)/2 // : 1

x^4 = (5^(1/2)+3)/2

x^4 = (5^(1/2)+3)/2 // ^ 1/4

abs(x) = ((5^(1/2)+3)^(1/4))/(2^(1/4))

x = ((5^(1/2)+3)^(1/4))/(2^(1/4)) or x = -(((5^(1/2)+3)^(1/4))/(2^(1/4)))

x in { ((3-5^(1/2))^(1/4))/(2^(1/4)), -(((3-5^(1/2))^(1/4))/(2^(1/4))), ((5^(1/2)+3)^(1/4))/(2^(1/4)), -(((5^(1/2)+3)^(1/4))/(2^(1/4))) }

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