5x^2-1/x^2

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Solution for 5x^2-1/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

t_1 = x^2

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

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

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

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

t_1^1

5*t_1^2-1 = 0

5*t_1^2-1 = 0

DELTA = 0^2-(-1*4*5)

DELTA = 20

DELTA > 0

t_1 = (20^(1/2)+0)/(2*5) or t_1 = (0-20^(1/2))/(2*5)

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

t_1 in { (-5^(1/2))/5, (1*5^(1/2))/5} 

t_1 = (-5^(1/2))/5

x^2-((-5^(1/2))/5) = 0

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

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

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

abs(x) = 5^(-1/4)

x = 5^(-1/4) or x = -5^(-1/4)

t_1 = (1*5^(1/2))/5

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

x^2-((5^(1/2))/5) = 0

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

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

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

abs(x) = 5^(-1/4)

x = 5^(-1/4) or x = -5^(-1/4)

x in { 5^(-1/4), -5^(-1/4), 5^(-1/4), -5^(-1/4) }

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