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

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


D( x )

x^4 = 0

x^2 = 0

x^4 = 0

x^4 = 0

1*x^4 = 0 // : 1

x^4 = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

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

t_1 = x^-2

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

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

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

DELTA = 49

DELTA > 0

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

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

-2 < 0

1/(x^2) = 1/4 // * x^2

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

4 = x^2

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

t_1 = 2

x^-2-2 = 0

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

x^-2 = 2

-2 < 0

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

1 = 2*x^2 // : 2

1/2 = x^2

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

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

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

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

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