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

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Solution for x^4-x^2-(1/4) equation: 


x in (-oo:+oo)

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

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

t_1 = x^2

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

t_1^2-t_1-1/4 = 0

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

DELTA = 2

DELTA > 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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