What kind of a Triangle is this???

Level 2

Let ABC be a triangle such that ∠ \angle ACB= π \pi /6 and let a,b,c denote the lengths of the sides opposite to A,B and C respectively. The value of x for which

a= x 2 + x + 1 x^{2}+x+1

b= x 2 − 1 x^{2}-1

c= 2 x + 1 2x+1

3 + 1 \sqrt{3}+1 -(2+ 3 \sqrt{3} ) 4 3 \sqrt{3} 2+ 3 \sqrt{3}

Anirudha Nayak by Anirudha Nayak , 24, India

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