(5x^3-10x)/(5x^3)

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Solution for (5x^3-10x)/(5x^3) equation:


D( x )

5*x^3 = 0

5*x^3 = 0

5*x^3 = 0

5*x^3 = 0 // : 5

x^3 = 0

x = 0

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

(5*x^3-(10*x))/(5*x^3) = 0

(5*x^3-10*x)/(5*x^3) = 0

5*x^3-10*x = 0

5*x*(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)

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

(5*x*(x-2^(1/2))*(x+2^(1/2)))/(5*x^3) = 0

( 5*x )

5*x = 0 // : 5

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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