Solve the equation :
${27 x}^{2} - 10 x + 1 = 0$

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Solution

The given quadratic equation is ${27 x}^{2} - 10 x + 1 = 0$
On comparing this equation with ${a x}^{2} + b x + c = 0$ ,
we obtain $a = 27, b = - 10,$ and $c = 1$
Therefore, the discriminant of the given equation is
$D = b^{2} - 4 a c = {(- 10)}^{2} - 4 \times 27 \times 1 = 100 - 108 = - 8$
Therefore, the required solutions are
$\frac{- b \pm \sqrt{D}}{2 a} = \frac{- (- 10) \pm \sqrt{- 8}}{2 \times 27} = \frac{10 \pm 2 \sqrt{2} i}{54}$
$= \frac{5 \pm \sqrt{2} i}{27} = \frac{5}{27} \pm \frac{\sqrt{2}}{27} i$

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