r^2-(4/r^2)=-1

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Solution for r^2-(4/r^2)=-1 equation: 


D( r )

r^2 = 0

r^2 = 0

r^2 = 0

1*r^2 = 0 // : 1

r^2 = 0

r = 0

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

r^2-(4/(r^2)) = -1 // + 1

r^2-(4/(r^2))+1 = 0

r^2-4*r^-2+1 = 0

t_1 = r^2

1*t_1^1-4*t_1^-1+1 = 0

1*t_1^1-4*t_1^-1+1*t_1^0 = 0

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

t_1^1*(1*t_1^2+1*t_1^1-4*t_1^0) = 0

t_1^1

t_1^2+t_1-4 = 0

t_1^2+t_1-4 = 0

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

DELTA = 17

DELTA > 0

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

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

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

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

r^2-((-(17^(1/2)+1))/2) = 0

r^2+(1/2)*(17^(1/2)+1) = 0

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

r^2 = -1/2*(17^(1/2)+1)

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

r^2-((17^(1/2)-1)/2) = 0

1*r^2 = (17^(1/2)-1)/2 // : 1

r^2 = (17^(1/2)-1)/2

r^2 = (17^(1/2)-1)/2 // ^ 1/2

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

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

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

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