-2x^2/x^4+2x^2+1

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Solution for -2x^2/x^4+2x^2+1 equation: 


D( x )

x^4 = 0

x^4 = 0

x^4 = 0

1*x^4 = 0 // : 1

x^4 = 0

x = 0

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

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

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

t_1 = x^2

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

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

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

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

t_1^1

2*t_1^2+t_1-2 = 0

2*t_1^2+t_1-2 = 0

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

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)-1)/(2*2) or t_1 = (-17^(1/2)-1)/(2*2)

t_1 = (17^(1/2)-1)/4 or t_1 = (-(17^(1/2)+1))/4

t_1 in { (-(17^(1/2)+1))/4, (17^(1/2)-1)/4} 

t_1 = (-(17^(1/2)+1))/4

x^2-((-(17^(1/2)+1))/4) = 0

x^2+(1/4)*(17^(1/2)+1) = 0

1*x^2 = -(1/4*(17^(1/2)+1)) // : 1

x^2 = -1/4*(17^(1/2)+1)

t_1 = (17^(1/2)-1)/4

x^2-((17^(1/2)-1)/4) = 0

1*x^2 = (17^(1/2)-1)/4 // : 1

x^2 = (17^(1/2)-1)/4

x^2 = (17^(1/2)-1)/4 // ^ 1/2

abs(x) = ((17^(1/2)-1)^(1/2))/2

x = ((17^(1/2)-1)^(1/2))/2 or x = -(((17^(1/2)-1)^(1/2))/2)

x in { ((17^(1/2)-1)^(1/2))/2, -(((17^(1/2)-1)^(1/2))/2) }

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