1+1/x^2-20/x^4=0

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Solution for 1+1/x^2-20/x^4=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)

1/(x^2)-(20/(x^4))+1 = 0

1/(x^2)-20*x^-4+1 = 0

x^-2-20*x^-4+1 = 0

t_1 = x^-2

1*t_1^1-20*t_1^2+1 = 0

t_1-20*t_1^2+1 = 0

DELTA = 1^2-(-20*1*4)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)-1)/(-20*2) or t_1 = (-81^(1/2)-1)/(-20*2)

t_1 = -1/5 or t_1 = 1/4

t_1 = -1/5

x^-2+1/5 = 0

1*x^-2 = -1/5 // : 1

x^-2 = -1/5

-2 < 0

1/(x^2) = -1/5 // * x^2

1 = -1/5*x^2 // : -1/5

-5 = x^2

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

x in { 2, -2 }

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