Ответ:

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Пошаговое объяснение:

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х ≠ 0

[tex]3x - \frac{1}{x} - 4 = 0 \\ \frac{3 {x}^{2} - 4x - 1 }{x} = 0 \\ 3 {x}^{2} - 4x - 1 = 0 \\ a =3 \\ b = - 4\\ c = - 1\\ D = {b}^{2} - 4ac = ( - 4) {}^{2} - 4 \times 3 \times( - 1) = \\ = 16 + 12 = 28 \: \: ( \sqrt{D} = 2 \sqrt{7}) \\ x_{1} = \frac{4 + 2 \sqrt{7} }{2 \times 3} = \frac{2(2 + \sqrt{7}) }{2 \times 3} = \frac{2 + \sqrt{7} }{3} \\ x_{2} = \frac{4 - 2 \sqrt{7} }{2 \times 3} = \frac{2(2 - \sqrt{7}) }{2 \times 3} = \frac{2 - \sqrt{7} }{3} [/tex]