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Problem
Problem
Let
A
B
C
ABC
A
B
C
be a triangle such that
∠
A
C
B
=
π
6
\angle ACB = \frac{\pi}{6}
∠
A
C
B
=
6
π
. If
a
,
b
a, b
a
,
b
and
c
c
c
denote the lengths of the sides opposite to
A
,
B
A, B
A
,
B
and
C
C
C
, respectively, then find the value(s) of
x
x
x
for which
a
=
x
2
+
x
+
1
a = x^2 + x + 1
a
=
x
2
+
x
+
1
,
b
=
x
2
−
1
b = x^2 - 1
b
=
x
2
−
1
and
c
=
2
x
+
1
c = 2x + 1
c
=
2
x
+
1
. a.
−
(
2
+
3
)
-(2 + \sqrt{3})
−
(
2
+
3
)
b.
1
+
3
1 + \sqrt{3}
1
+
3
c.
2
+
3
2 + \sqrt{3}
2
+
3
d.
4
3
4\sqrt{3}
4
3
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