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

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Solution for (x-2)^3/2-3(x-2)^1/2=0 equation: 


x in (-oo:+oo)

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

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

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

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

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

x^3-6*x^2+9*x-2 = 0

x^3-6*x^2+9*x-2 = 0

x^3-6*x^2+9*x-2 = 0

{ 1, -1, 2, -2 }

1

x = 1

x^3-6*x^2+9*x-2 = 2

1

-1

x = -1

x^3-6*x^2+9*x-2 = -18

-1

2

x = 2

x^3-6*x^2+9*x-2 = 0

2

x-2

x^2-4*x+1

x^3-6*x^2+9*x-2

x-2

2*x^2-x^3

9*x-4*x^2-2

4*x^2-8*x

x-2

2-x

0

x^2-4*x+1 = 0

DELTA = (-4)^2-(1*1*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)+4)/(1*2) or x = (4-12^(1/2))/(1*2)

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

x in { (4-2*3^(1/2))/2, (2*3^(1/2)+4)/2, 2} 

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

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

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

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

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

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

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

( x-((4-2*3^(1/2))/2) )

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

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

( x-2 )

x-2 = 0 // + 2

x = 2

x in { (2*3^(1/2)+4)/2, (4-2*3^(1/2))/2, 2 }

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