Let be a triangle such that

MATHEMATICS · Single correct · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Let

ABC

be a triangle such that

\angle ACB=\frac{\pi}{6}

. If

a

b

, and

c

denote the lengths of the sides opposite to

A

B

, and

C

, respectively, find the value of

x

for which

a=x^2+x+1

b=x^2-1

, and

c=2x+1

. (1)

-(2+\sqrt{3})

(2)

1+\sqrt{3}

(3)

2+\sqrt{3}

(4)

4\sqrt{3}