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

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Solution for 1/4*x^4+x^2-2=0 equation: 


x in (-oo:+oo)

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

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

t_1 = x^2

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

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

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

DELTA = 3

DELTA > 0

t_1 = (3^(1/2)-1)/(1/4*2) or t_1 = (-3^(1/2)-1)/(1/4*2)

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

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

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

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

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

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

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

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

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

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

x^2 = 2*(3^(1/2)-1)

x^2 = 2*(3^(1/2)-1) // ^ 1/2

abs(x) = 2^(1/2)*(3^(1/2)-1)^(1/2)

x = 2^(1/2)*(3^(1/2)-1)^(1/2) or x = -(2^(1/2)*(3^(1/2)-1)^(1/2))

x in { 2^(1/2)*(3^(1/2)-1)^(1/2), -(2^(1/2)*(3^(1/2)-1)^(1/2)) }

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