(3/x^2)-(54/x^4)

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Solution for (3/x^2)-(54/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)

3/(x^2)-(54/(x^4)) = 0

3/(x^2)-54*x^-4 = 0

3*x^-2-54*x^-4 = 0

t_1 = x^-2

3*t_1^1-54*t_1^2 = 0

3*t_1-54*t_1^2 = 0

DELTA = 3^2-(-54*0*4)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)-3)/(-54*2) or t_1 = (-9^(1/2)-3)/(-54*2)

t_1 = 0 or t_1 = 1/18

t_1 = 0

x^-2+0 = 0

x^-2 = 0

1*x^-2 = 0 // : 1

x^-2 = 0

x należy do O

t_1 = 1/18

x^-2-1/18 = 0

1*x^-2 = 1/18 // : 1

x^-2 = 1/18

-2 < 0

1/(x^2) = 1/18 // * x^2

1 = 1/18*x^2 // : 1/18

18 = x^2

x^2 = 18 // ^ 1/2

abs(x) = 3*2^(1/2)

x = 3*2^(1/2) or x = -(3*2^(1/2))

x in { 3*2^(1/2), -(3*2^(1/2)) }

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