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

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


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

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

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

t_1 = x^(1/2)

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

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

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

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

t_1^2

16*t_1^3-2 = 0

{ 1, -1, 2, -2 }

1

t_1 = 1

16*t_1^3-2 = 14

1

-1

t_1 = -1

16*t_1^3-2 = -18

-1

2

t_1 = 2

16*t_1^3-2 = 126

2

-2

t_1 = -2

16*t_1^3-2 = -130

-2

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

1/2

t_1

1/2

16*t_1^3-2 = 0

1/2

t_1-1/2

16*t_1^2+8*t_1+4

16*t_1^3-2

t_1-1/2

8*t_1^2-16*t_1^3

8*t_1^2-2

4*t_1-8*t_1^2

4*t_1-2

2-4*t_1

0

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

DELTA = 8^2-(4*4*16)

DELTA = -192

DELTA < 0

t_1 in { 1/2}

t_1 = 1/2

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

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

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

x^(1/2) = 1/2

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

x = 1/4

x = 1/4

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