(12x^6-24x^4)/(4x^3)

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Solution for (12x^6-24x^4)/(4x^3) equation:


D( x )

4*x^3 = 0

4*x^3 = 0

4*x^3 = 0

4*x^3 = 0 // : 4

x^3 = 0

x = 0

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

(12*x^6-(24*x^4))/(4*x^3) = 0

(12*x^6-24*x^4)/(4*x^3) = 0

12*x^6-24*x^4 = 0

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

1*x^2 = 2 // : 1

x^2 = 2

x^2 = 2 // ^ 1/2

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

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

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

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

( 12*x^4 )

12*x^4 = 0 // : 12

x^4 = 0

x = 0

( x+2^(1/2) )

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

x = -2^(1/2)

( x-2^(1/2) )

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

x = 2^(1/2)

x in { 0}

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

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