(9x^2)-(1/(8x^2))-4=0

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Solution for (9x^2)-(1/(8x^2))-4=0 equation:


D( x )

8*x^2 = 0

8*x^2 = 0

8*x^2 = 0

8*x^2 = 0 // : 8

x^2 = 0

x = 0

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

9*x^2-(1/(8*x^2))-4 = 0

9*x^2+(-1/8)*x^-2-4 = 0

9*x^2-1/8*x^-2-4 = 0

t_1 = x^2

9*t_1^1-1/8*t_1^-1-4 = 0

9*t_1^1-1/8*t_1^-1-4*t_1^0 = 0

(9*t_1^2-4*t_1^1-1/8*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(9*t_1^2-4*t_1^1-1/8*t_1^0) = 0

t_1^1

9*t_1^2-4*t_1-1/8 = 0

9*t_1^2-4*t_1-1/8 = 0

DELTA = (-4)^2-(4*9*(-1/8))

DELTA = 41/2

DELTA > 0

t_1 = ((41/2)^(1/2)+4)/(2*9) or t_1 = (4-(41/2)^(1/2))/(2*9)

t_1 = ((41/2)^(1/2)+4)/18 or t_1 = (4-(41/2)^(1/2))/18

t_1 in { (4-(41/2)^(1/2))/18, ((41/2)^(1/2)+4)/18}

t_1 = (4-(41/2)^(1/2))/18

x^2-((4-(41/2)^(1/2))/18) = 0

1*x^2 = (4-(41/2)^(1/2))/18 // : 1

x^2 = (4-(41/2)^(1/2))/18

t_1 = ((41/2)^(1/2)+4)/18

x^2-(((41/2)^(1/2)+4)/18) = 0

1*x^2 = ((41/2)^(1/2)+4)/18 // : 1

x^2 = ((41/2)^(1/2)+4)/18

x^2 = ((41/2)^(1/2)+4)/18 // ^ 1/2

abs(x) = (((41/2)^(1/2)+4)^(1/2))/(3*2^(1/2))

x = (((41/2)^(1/2)+4)^(1/2))/(3*2^(1/2)) or x = -((((41/2)^(1/2)+4)^(1/2))/(3*2^(1/2)))

x in { (((41/2)^(1/2)+4)^(1/2))/(3*2^(1/2)), -((((41/2)^(1/2)+4)^(1/2))/(3*2^(1/2))) }

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