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

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


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

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

t_1 = x^(1/2)

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

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

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

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

t_1^1

t_1^3-2*t_1+1 = 0

{ 1, -1 }

1

t_1 = 1

t_1^3-2*t_1+1 = 0

1

t_1-1

t_1^2+t_1-1

t_1^3-2*t_1+1

t_1-1

t_1^2-t_1^3

t_1^2-2*t_1+1

t_1-t_1^2

1-t_1

t_1-1

0

t_1^2+t_1-1 = 0

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

DELTA = 5

DELTA > 0

t_1 = (5^(1/2)-1)/(1*2) or t_1 = (-5^(1/2)-1)/(1*2)

t_1 = (5^(1/2)-1)/2 or t_1 = (-(5^(1/2)+1))/2

t_1 in { (-(5^(1/2)+1))/2, (5^(1/2)-1)/2, 1} 

t_1 = (-(5^(1/2)+1))/2

x^(1/2)-((-(5^(1/2)+1))/2) = 0

x^(1/2)+(1/2)*(5^(1/2)+1) = 0

1*x^(1/2) = -(1/2*(5^(1/2)+1)) // : 1

x^(1/2) = -1/2*(5^(1/2)+1)

( -1/2*(5^(1/2)+1) < 0 i 1/2 in (0:1) ) => x naleu017Cy do O

t_1 = (5^(1/2)-1)/2

x^(1/2)-((5^(1/2)-1)/2) = 0

1*x^(1/2) = (5^(1/2)-1)/2 // : 1

x^(1/2) = (5^(1/2)-1)/2

x^(1/2) = (5^(1/2)-1)/2 // ^ 2

x = ((5^(1/2)-1)^2)/4

t_1 = 1

x^(1/2)-1 = 0

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

x^(1/2) = 1

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

x = 1

x in { ((5^(1/2)-1)^2)/4, 1 }

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