3/4=2x-4/x

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Solution for 3/4=2x-4/x equation:


D( x )

x = 0

x = 0

x = 0

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

3/4 = 2*x-(4/x) // - 2*x-(4/x)

4/x-(2*x)+3/4 = 0

4/x-2*x+3/4 = 0

4*x^-1-2*x^1+3/4*x^0 = 0

(3/4*x^1-2*x^2+4*x^0)/(x^1) = 0 // * x^2

x^1*(3/4*x^1-2*x^2+4*x^0) = 0

x^1

(3/4)*x-2*x^2+4 = 0

(3/4)*x-2*x^2+4 = 0

DELTA = (3/4)^2-(-2*4*4)

DELTA = 521/16

DELTA > 0

x = ((521/16)^(1/2)-(3/4))/(-2*2) or x = (-(3/4)-(521/16)^(1/2))/(-2*2)

x = ((521/16)^(1/2)-3/4)/(-4) or x = ((521/16)^(1/2)+3/4)/4

x in { ((521/16)^(1/2)-3/4)/(-4), ((521/16)^(1/2)+3/4)/4}

x in { ((521/16)^(1/2)-3/4)/(-4), ((521/16)^(1/2)+3/4)/4 }

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