p^2-1/p^2-4

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Solution for p^2-1/p^2-4 equation: 


D( p )

p^2 = 0

p^2 = 0

p^2 = 0

1*p^2 = 0 // : 1

p^2 = 0

p = 0

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

p^2-(1/(p^2))-4 = 0

p^2-p^-2-4 = 0

t_1 = p^2

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

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

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

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

t_1^1

t_1^2-4*t_1-1 = 0

t_1^2-4*t_1-1 = 0

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

DELTA = 20

DELTA > 0

t_1 = (20^(1/2)+4)/(1*2) or t_1 = (4-20^(1/2))/(1*2)

t_1 = (2*5^(1/2)+4)/2 or t_1 = (4-2*5^(1/2))/2

t_1 in { (4-2*5^(1/2))/2, (2*5^(1/2)+4)/2} 

t_1 = (4-2*5^(1/2))/2

p^2-((4-2*5^(1/2))/2) = 0

1*p^2 = (4-2*5^(1/2))/2 // : 1

p^2 = (4-2*5^(1/2))/2

t_1 = (2*5^(1/2)+4)/2

p^2-((2*5^(1/2)+4)/2) = 0

1*p^2 = (2*5^(1/2)+4)/2 // : 1

p^2 = (2*5^(1/2)+4)/2

p^2 = (2*5^(1/2)+4)/2 // ^ 1/2

abs(p) = ((2*5^(1/2)+4)^(1/2))/(2^(1/2))

p = ((2*5^(1/2)+4)^(1/2))/(2^(1/2)) or p = -(((2*5^(1/2)+4)^(1/2))/(2^(1/2)))

p in { ((2*5^(1/2)+4)^(1/2))/(2^(1/2)), -(((2*5^(1/2)+4)^(1/2))/(2^(1/2))) }

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