1/3-1/x^2=5/3x^2+3/x^4

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Solution for 1/3-1/x^2=5/3x^2+3/x^4 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)

1/3-(1/(x^2)) = (5/3)*x^2+3/(x^4) // - (5/3)*x^2+3/(x^4)

1/3-((5/3)*x^2)-(1/(x^2))-(3/(x^4)) = 0

(-5/3)*x^2-x^-2-3*x^-4+1/3 = 0

1/3-5/3*x^2-x^-2-3*x^-4 = 0

t_1 = x^2

1/3-5/3*t_1^1-1*t_1^-1-3*t_1^-2 = 0

1/3*t_1^0-5/3*t_1^1-1*t_1^-1-3*t_1^-2 = 0

(1/3*t_1^2-5/3*t_1^3-1*t_1^1-3*t_1^0)/(t_1^2) = 0 // * t_1^4

t_1^2*(1/3*t_1^2-5/3*t_1^3-1*t_1^1-3*t_1^0) = 0

t_1^2

(-5/3)*t_1^3+(1/3)*t_1^2-t_1-3 = 0

(-5/3)*t_1^3+(1/3)*t_1^2-t_1-3 = 0 // * 0

{ 1, -1, 3, -3, 9, -9 }

1

t_1 = 1

t_1^2-5*t_1^3-3*t_1-9 = -16

1

-1

t_1 = -1

t_1^2-5*t_1^3-3*t_1-9 = 0

-1

t_1+1

6*t_1-5*t_1^2-9

t_1^2-5*t_1^3-3*t_1-9

t_1+1

5*t_1^3+5*t_1^2

6*t_1^2-3*t_1-9

-6*t_1^2-6*t_1

-9*t_1-9

9*t_1+9

0

6*t_1-5*t_1^2-9 = 0

DELTA = 6^2-(-9*(-5)*4)

DELTA = -144

DELTA < 0

t_1 in { -1} 

t_1 = -1

x^2+1 = 0

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

x^2 = -1

x belongs to the empty set

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