(12x^6-9x^4)/(3x^3)

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Solution for (12x^6-9x^4)/(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)

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

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

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

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

4*x^2 = 3 // : 4

x^2 = 3/4

x^2 = 3/4 // ^ 1/2

abs(x) = (3/4)^(1/2)

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

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

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

( 3*x^4 )

3*x^4 = 0 // : 3

x^4 = 0

x = 0

( x+(3/4)^(1/2) )

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

x = -(3/4)^(1/2)

( x-(3/4)^(1/2) )

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

x = (3/4)^(1/2)

x in { 0}

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

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