((9x^4)-(27x^6))/(3x^3)

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Solution for ((9x^4)-(27x^6))/(3x^3) equation:


D( x )

3*x^3 = 0

3*x^3 = 0

3*x^3 = 0

3*x^3 = 0 // : 3

x^3 = 0

x = 0

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

(9*x^4-(27*x^6))/(3*x^3) = 0

(9*x^4-27*x^6)/(3*x^3) = 0

9*x^4-27*x^6 = 0

9*x^4*(1-3*x^2) = 0

-3*x^2 = -1 // : -3

x^2 = 1/3

x^2 = 1/3 // ^ 1/2

abs(x) = (1/3)^(1/2)

x = (1/3)^(1/2) or x = -(1/3)^(1/2)

9*x^4*(x-(1/3)^(1/2))*(x+(1/3)^(1/2)) = 0

(9*x^4*(x-(1/3)^(1/2))*(x+(1/3)^(1/2)))/(3*x^3) = 0

( 9*x^4 )

9*x^4 = 0 // : 9

x^4 = 0

x = 0

( x+(1/3)^(1/2) )

x+(1/3)^(1/2) = 0 // - (1/3)^(1/2)

x = -(1/3)^(1/2)

( x-(1/3)^(1/2) )

x-(1/3)^(1/2) = 0 // + (1/3)^(1/2)

x = (1/3)^(1/2)

x in { 0}

x in { -(1/3)^(1/2), (1/3)^(1/2) }

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