1/(1/X+1/2X)=3

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Solution for 1/(1/X+1/2X)=3 equation: 


D( X )

(1/2)*X+1/X = 0

X = 0

(1/2)*X+1/X = 0

(1/2)*X+1/X = 0

1/2*X^1+1*X^-1 = 0

(1/2*X^2+1*X^0)/(X^1) = 0 // * X^2

X^1*(1/2*X^2+1*X^0) = 0

X^1

(1/2)*X^2+1 = 0

(1/2)*X^2+1 = 0

DELTA = 0^2-(1*4*(1/2))

DELTA = -2

DELTA < 0

X in { } 

X = 0

X = 0

X in (-oo:0) U (0:+oo)

1/((1/2)*X+1/X) = 3 // - 3

1/((1/2)*X+1/X)-3 = 0

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

1/2*X+X^-1 = 0

1/2*X+X^-1 = 0

X^-1*(1/2*X^2+1) = 0

1/2*X^2 = -1 // : 1/2

X^2 = -2

1/X = 0

1/(X^-1)-3 = 0

1/(X^-1)+(-3*X^-1)/(X^-1) = 0

1-3*X^-1 = 0

(1-3*X^-1)/(X^-1) = 0

(1-3*X^-1)/(X^-1) = 0 // * 1/X

1-3*X^-1 = 0

-3*X^-1 = -1 // : -3

X^-1 = 1/3

-1 < 0

1/(X^1) = 1/3 // * X^1

1 = 1/3*X^1 // : 1/3

3 = X^1

X = 3

X = 3

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