(3x-2)^2/3=(8x0)^1/3

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Solution for (3x-2)^2/3=(8x0)^1/3 equation:


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

9*x^2-12*x-4 = 0

9*x^2-12*x-4 = 0

9*x^2-12*x-4 = 0

DELTA = (-12)^2-(-4*4*9)

DELTA = 288

DELTA > 0

x = (288^(1/2)+12)/(2*9) or x = (12-288^(1/2))/(2*9)

x = (12*2^(1/2)+12)/18 or x = (12-12*2^(1/2))/18

(x-((12-12*2^(1/2))/18))*(x-((12*2^(1/2)+12)/18)) = 0

((x-((12-12*2^(1/2))/18))*(x-((12*2^(1/2)+12)/18)))/3 = 0

((x-((12-12*2^(1/2))/18))*(x-((12*2^(1/2)+12)/18)))/3 = 0 // * 3

(x-((12-12*2^(1/2))/18))*(x-((12*2^(1/2)+12)/18)) = 0

( x-((12*2^(1/2)+12)/18) )

x-((12*2^(1/2)+12)/18) = 0 // + (12*2^(1/2)+12)/18

x = (12*2^(1/2)+12)/18

( x-((12-12*2^(1/2))/18) )

x-((12-12*2^(1/2))/18) = 0 // + (12-12*2^(1/2))/18

x = (12-12*2^(1/2))/18

x in { (12*2^(1/2)+12)/18, (12-12*2^(1/2))/18 }

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