(-6x^9+12x^7)/x^12

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Solution for (-6x^9+12x^7)/x^12 equation:


D( x )

x^12 = 0

x^12 = 0

x^12 = 0

1*x^12 = 0 // : 1

x^12 = 0

x = 0

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

(12*x^7-6*x^9)/(x^12) = 0

12*x^7-6*x^9 = 0

6*x^7*(2-x^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)

6*x^7*(x-2^(1/2))*(x+2^(1/2)) = 0

(6*x^7*(x-2^(1/2))*(x+2^(1/2)))/(x^12) = 0

( 6*x^7 )

6*x^7 = 0 // : 6

x^7 = 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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