(192x^2-x^4)/(4x)

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Solution for (192x^2-x^4)/(4x) equation:


D( x )

4*x = 0

4*x = 0

4*x = 0

4*x = 0 // : 4

x = 0

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

(192*x^2-x^4)/(4*x) = 0

192*x^2-x^4 = 0

x^2*(192-x^2) = 0

-1*x^2 = -192 // : -1

x^2 = 192

x^2 = 192 // ^ 1/2

abs(x) = 8*3^(1/2)

x = 8*3^(1/2) or x = -(8*3^(1/2))

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

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

( x+8*3^(1/2) )

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

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

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

( x-8*3^(1/2) )

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

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

x = 8*3^(1/2)

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 0}

x in { -8*3^(1/2), 8*3^(1/2) }

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