Solve the following equation:
$x^{3} + 21 x + 342 = 0$ .

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Solution

Given equation, $x^{3} + 21 x + 342 = 0$

$\Rightarrow x^{3} - 6 x^{2} + 6 x^{2} + 57 x - 36 x + 342 = 0$
$\Rightarrow (x + 6) (x^{2} - 6 x + 57) = 0$
Hence, $x + 6 = 0$ and $x^{2} - 6 x + 57 = 0$
Therefore, $x = - 6 and x = \frac{6 \pm \sqrt{36 - 4 \times 57}}{2} = 3 \pm 4 \sqrt{3} i$
Thus roots of the given equation are $x = - 6, 3 \pm 4 \sqrt{3} i$

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