x^4-9/4x^2+1/2=0

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Solution for x^4-9/4x^2+1/2=0 equation: 


x in (-oo:+oo)

x^4-((9/4)*x^2)+1/2 = 0

x^4+(-9/4)*x^2+1/2 = 0

x^4-9/4*x^2+1/2 = 0

t_1 = x^2

1*t_1^2-9/4*t_1^1+1/2 = 0

t_1^2-9/4*t_1+1/2 = 0

DELTA = (-9/4)^2-(1/2*1*4)

DELTA = 49/16

DELTA > 0

t_1 = ((49/16)^(1/2)+9/4)/(1*2) or t_1 = (9/4-(49/16)^(1/2))/(1*2)

t_1 = 2 or t_1 = 1/4

t_1 = 1/4

x^2-1/4 = 0

1*x^2 = 1/4 // : 1

x^2 = 1/4

x^2 = 1/4 // ^ 1/2

abs(x) = 1/2

x = 1/2 or x = -1/2

t_1 = 2

x^2-2 = 0

1*x^2 = 2 // : 1

x^2 = 2

x^2 = 2 // ^ 1/2

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

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

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

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