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

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Solution for x^2+(5/x^2)=5 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)

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

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

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

t_1 = x^2

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

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

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

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

t_1^1

t_1^2-5*t_1+5 = 0

t_1^2-5*t_1+5 = 0

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

DELTA = 5

DELTA > 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

x in { ((5-5^(1/2))^(1/2))/(2^(1/2)), -(((5-5^(1/2))^(1/2))/(2^(1/2))), ((5^(1/2)+5)^(1/2))/(2^(1/2)), -(((5^(1/2)+5)^(1/2))/(2^(1/2))) }

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