3y^2-3/y^2-1

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Solution for 3y^2-3/y^2-1 equation: 


D( y )

y^2 = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

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

3*y^2-(3/(y^2))-1 = 0

3*y^2-3*y^-2-1 = 0

t_1 = y^2

3*t_1^1-3*t_1^-1-1 = 0

3*t_1^1-3*t_1^-1-1*t_1^0 = 0

(3*t_1^2-1*t_1^1-3*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(3*t_1^2-1*t_1^1-3*t_1^0) = 0

t_1^1

3*t_1^2-t_1-3 = 0

3*t_1^2-t_1-3 = 0

DELTA = (-1)^2-(-3*3*4)

DELTA = 37

DELTA > 0

t_1 = (37^(1/2)+1)/(2*3) or t_1 = (1-37^(1/2))/(2*3)

t_1 = (37^(1/2)+1)/6 or t_1 = (1-37^(1/2))/6

t_1 in { (1-37^(1/2))/6, (37^(1/2)+1)/6} 

t_1 = (1-37^(1/2))/6

y^2-((1-37^(1/2))/6) = 0

1*y^2 = (1-37^(1/2))/6 // : 1

y^2 = (1-37^(1/2))/6

t_1 = (37^(1/2)+1)/6

y^2-((37^(1/2)+1)/6) = 0

1*y^2 = (37^(1/2)+1)/6 // : 1

y^2 = (37^(1/2)+1)/6

y^2 = (37^(1/2)+1)/6 // ^ 1/2

abs(y) = ((37^(1/2)+1)^(1/2))/(6^(1/2))

y = ((37^(1/2)+1)^(1/2))/(6^(1/2)) or y = -(((37^(1/2)+1)^(1/2))/(6^(1/2)))

y in { ((37^(1/2)+1)^(1/2))/(6^(1/2)), -(((37^(1/2)+1)^(1/2))/(6^(1/2))) }

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