Question

Find the roots of the quadratic equation x - 1/3x = 1/6

Answer 1

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$= > x - \frac{1}{3x} = \frac{1}{6} \\ \\ = > \frac{3x {}^{2} - 1 }{3x} = \frac{1}{6} \\ \\ = > 6(3x {}^{2} - 1) = 3x \\ \\ = > 18x {}^{2} - 6 = 3x \\ \\ = > 18x {}^{2} - 3x - 6 = 0 \\ \\ = > 3(6x {}^{2} - x - 2) = 0 \\ \\ = > 6 x{}^{2} - 4x + 3x - 2 = 0 \\ \\ = >2x(3x - 2) + 1(3x - 2) = 0 \\ \\ = > (2x + 1)(3x - 2) = 0 \\ \\ x = \frac{ - 1}{2} \: and \: x = \frac{2}{3 } \\ \\ so \: the \: roots \: are \: \frac{ - 1}{2} and \: \frac{2}{3}$
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Answer 2

Answer:

$x - \frac{1}{3x} = \frac{1}{6}$

$= > \frac{ {3x}^{2} - 1}{3x} = \frac{1}{6} \\ = > 6( {3x}^{2} - 1) = 3x \\ = > {18x}^{2} - 6 = 3x \\ = > {18x}^{2} - 3x - 6 = 0 \\ = > 3( {6x}^{2} - x - 2) \\ = > {6x}^{2} - 4x + 3x - 2 = 0 \\ = > 2x(3x - 2) + (3x - 2) \\ = > (2x + 1)(3x - 2)$

$x = \frac{ - 1}{2 } \: and \: x = \frac{2}{3}$