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Mathematics
Problem
Let
x
1
,
x
2
,
x
3
x_1, x_2, x_3
x
1
,
x
2
,
x
3
be the solution of
tan
−
1
(
2
x
+
1
x
+
1
)
+
tan
−
1
(
2
x
−
1
x
−
1
)
=
2
tan
−
1
(
x
+
1
)
\tan^{-1}\left(\frac{2x+1}{x+1}\right) + \tan^{-1}\left(\frac{2x-1}{x-1}\right) = 2\tan^{-1}(x+1)
tan
−
1
(
x
+
1
2
x
+
1
)
+
tan
−
1
(
x
−
1
2
x
−
1
)
=
2
tan
−
1
(
x
+
1
)
where
x
1
<
x
2
<
x
3
x_1 < x_2 < x_3
x
1
<
x
2
<
x
3
, then
2
x
1
+
x
2
+
x
3
2
2x_1 + x_2 + x_3^2
2
x
1
+
x
2
+
x
3
2
is equal to
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