(24x^6-16x^4)/(4x^3)

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Solution for (24x^6-16x^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)

(24*x^6-(16*x^4))/(4*x^3) = 0

(24*x^6-16*x^4)/(4*x^3) = 0

24*x^6-16*x^4 = 0

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

3*x^2 = 2 // : 3

x^2 = 2/3

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

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

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

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

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

( 8*x^4 )

8*x^4 = 0 // : 8

x^4 = 0

x = 0

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

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

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

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

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

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

x in { 0}

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

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