2/x^4-5/x^2+2=0

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Solution for 2/x^4-5/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)

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

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

2*x^-4-5*x^-2+2 = 0

t_1 = x^-2

2*t_1^2-5*t_1^1+2 = 0

2*t_1^2-5*t_1+2 = 0

DELTA = (-5)^2-(2*2*4)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+5)/(2*2) or t_1 = (5-9^(1/2))/(2*2)

t_1 = 2 or t_1 = 1/2

t_1 = 1/2

x^-2-1/2 = 0

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

x^-2 = 1/2

-2 < 0

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

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

2 = x^2

x^2 = 2 // ^ 1/2

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

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

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^(1/2), -2^(1/2), (1/2)^(1/2), -(1/2)^(1/2) }

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