(x^(1/2)/3)=(243/x)

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Solution for (x^(1/2)/3)=(243/x) equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

(x^(1/2))/3 = 243/x // - 243/x

(x^(1/2))/3-(243/x) = 0

(x^(1/2))/3-243*x^-1 = 0

1/3*x^(1/2)-243*x^-1 = 0

t_1 = x^(1/2)

1/3*t_1^1-243*t_1^-2 = 0

1/3*t_1^1-243*t_1^-2 = 0

(1/3*t_1^3-243*t_1^0)/(t_1^2) = 0 // * t_1^4

t_1^2*(1/3*t_1^3-243*t_1^0) = 0

t_1^2

(1/3)*t_1^3-243 = 0

(1/3)*t_1^3-243 = 0 // * 0

{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81, 243, -243, 729, -729 }

1

t_1 = 1

t_1^3-729 = -728

1

-1

t_1 = -1

t_1^3-729 = -730

-1

3

t_1 = 3

t_1^3-729 = -702

3

-3

t_1 = -3

t_1^3-729 = -756

-3

9

t_1 = 9

t_1^3-729 = 0

9

t_1-9

t_1^2+9*t_1+81

t_1^3-729

t_1-9

9*t_1^2-t_1^3

9*t_1^2-729

81*t_1-9*t_1^2

81*t_1-729

729-81*t_1

0

t_1^2+9*t_1+81 = 0

DELTA = 9^2-(1*4*81)

DELTA = -243

DELTA < 0

t_1 in { 9} 

t_1 = 9

x^(1/2)-9 = 0

1*x^(1/2) = 9 // : 1

x^(1/2) = 9

x^(1/2) = 9 // ^ 2

x = 81

x = 81

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