2x-16x^(-1/2)=0

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Solution for 2x-16x^(-1/2)=0 equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

2*x-(16*x^(-1/2)) = 0

2*x-16*x^(-1/2) = 0

t_1 = x^(1/2)

2*t_1^2-16*t_1^-1 = 0

(2*t_1^3-16*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2*t_1^3-16*t_1^0) = 0

t_1^1

2*t_1^3-16 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

t_1 = 1

2*t_1^3-16 = -14

1

-1

t_1 = -1

2*t_1^3-16 = -18

-1

2

t_1 = 2

2*t_1^3-16 = 0

2

t_1-2

2*t_1^2+4*t_1+8

2*t_1^3-16

t_1-2

4*t_1^2-2*t_1^3

4*t_1^2-16

8*t_1-4*t_1^2

8*t_1-16

16-8*t_1

0

2*t_1^2+4*t_1+8 = 0

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

DELTA = -48

DELTA < 0

t_1 in { 2} 

t_1 = 2

x^(1/2)-2 = 0

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

x^(1/2) = 2

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

x = 4

x = 4

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