(7/12)*y^3-(2/12)*y^-3

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Solution for (7/12)*y^3-(2/12)*y^-3 equation: 


D( y )

y = 0

y = 0

y = 0

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

(7/12)*y^3-((2/12)*y^-3) = 0

(7/12)*y^3+(-1/6)*y^-3 = 0

7/12*y^3-1/6*y^-3 = 0

t_1 = y^3

7/12*t_1^1-1/6*t_1^-1 = 0

7/12*t_1^1-1/6*t_1^-1 = 0

(7/12*t_1^2-1/6*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(7/12*t_1^2-1/6*t_1^0) = 0

t_1^1

(7/12)*t_1^2-1/6 = 0

(7/12)*t_1^2-1/6 = 0

DELTA = 0^2-(4*(7/12)*(-1/6))

DELTA = 7/18

DELTA > 0

t_1 = ((7/18)^(1/2)+0)/(2*(7/12)) or t_1 = (0-(7/18)^(1/2))/(2*(7/12))

t_1 = 6/7*(7/18)^(1/2) or t_1 = 6/7*(7/18)^(1/2)

t_1 in { 6/7*(7/18)^(1/2), 6/7*(7/18)^(1/2)} 

t_1 = 6/7*(7/18)^(1/2)

y^3-(6/7*(7/18)^(1/2)) = 0

y^3-6/7*(7/18)^(1/2) = 0

1*y^3 = -(-6/7*(7/18)^(1/2)) // : 1

y^3 = 6/7*(7/18)^(1/2)

y^3 = 6/7*(7/18)^(1/2) // ^ 1/3

y = (6/7)^(1/3)*(7/18)^(1/6)

t_1 = 6/7*(7/18)^(1/2)

y^3-(6/7*(7/18)^(1/2)) = 0

y^3-6/7*(7/18)^(1/2) = 0

1*y^3 = -(-6/7*(7/18)^(1/2)) // : 1

y^3 = 6/7*(7/18)^(1/2)

y^3 = 6/7*(7/18)^(1/2) // ^ 1/3

y = (6/7)^(1/3)*(7/18)^(1/6)

y in { (6/7)^(1/3)*(7/18)^(1/6), (6/7)^(1/3)*(7/18)^(1/6) }

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