x-8/(x^(1/2))=65

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Solution for x-8/(x^(1/2))=65 equation: 


D( x )

x < 0

x^(1/2) = 0

x < 0

x^(1/2) = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

x in (0:+oo)

x-(8/(x^(1/2))) = 65 // - 65

x-(8/(x^(1/2)))-65 = 0

x-8*x^(-(1/2))-65 = 0

x-8*x^(-1/2)-65 = 0

t_1 = x^(1/2)

1*t_1^2-8*t_1^-1-65 = 0

1*t_1^2-8*t_1^-1-65*t_1^0 = 0

(1*t_1^3-65*t_1^1-8*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^3-65*t_1^1-8*t_1^0) = 0

t_1^1

t_1^3-65*t_1-8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

t_1 = 1

t_1^3-65*t_1-8 = -72

1

-1

t_1 = -1

t_1^3-65*t_1-8 = 56

-1

2

t_1 = 2

t_1^3-65*t_1-8 = -130

2

-2

t_1 = -2

t_1^3-65*t_1-8 = 114

-2

4

t_1 = 4

t_1^3-65*t_1-8 = -204

4

-4

t_1 = -4

t_1^3-65*t_1-8 = 188

-4

8

t_1 = 8

t_1^3-65*t_1-8 = -16

8

-8

t_1 = -8

t_1^3-65*t_1-8 = 0

-8

t_1+8

t_1^2-8*t_1-1

t_1^3-65*t_1-8

t_1+8

-t_1^3-8*t_1^2

-8*t_1^2-65*t_1-8

8*t_1^2+64*t_1

-t_1-8

t_1+8

0

t_1^2-8*t_1-1 = 0

DELTA = (-8)^2-(-1*1*4)

DELTA = 68

DELTA > 0

t_1 = (68^(1/2)+8)/(1*2) or t_1 = (8-68^(1/2))/(1*2)

t_1 = (2*17^(1/2)+8)/2 or t_1 = (8-2*17^(1/2))/2

t_1 in { (8-2*17^(1/2))/2, (2*17^(1/2)+8)/2, -8} 

t_1 = (8-2*17^(1/2))/2

x^(1/2)-((8-2*17^(1/2))/2) = 0

1*x^(1/2) = (8-2*17^(1/2))/2 // : 1

x^(1/2) = (8-2*17^(1/2))/2

( (8-2*17^(1/2))/2 < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = (2*17^(1/2)+8)/2

x^(1/2)-((2*17^(1/2)+8)/2) = 0

1*x^(1/2) = (2*17^(1/2)+8)/2 // : 1

x^(1/2) = (2*17^(1/2)+8)/2

x^(1/2) = (2*17^(1/2)+8)/2 // ^ 2

x = ((2*17^(1/2)+8)^2)/4

t_1 = -8

x^(1/2)+8 = 0

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

x^(1/2) = -8

( -8 < 0 i 1/2 in (0:1) ) => x należy do O

x = ((2*17^(1/2)+8)^2)/4

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