Let \( \mathrm{ABC} \) be a triangle such that \( \angle \mathrm{AC...

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Let \( \mathrm{ABC} \) be a triangle such that \( \angle \mathrm{ACB}=\frac{\pi}{6} \) and let \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) denote the lengths of the sides opposite
P to \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) respectively. The value(s) of \( x \) for which \( \mathrm{a}=\mathrm{x}^{2}+\mathrm{x}+1, \mathrm{~b}=\mathrm{x}^{2}-1 \) and \( \mathrm{c}=2 \mathrm{x}+1 \) is/are

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(A) \( -(2+\sqrt{3}) \)
(B) \( 1+\sqrt{3} \)
(C) \( 2+\sqrt{3} \)
(D) \( 4 \sqrt{3} \)
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