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Problem
Show that
∣
a
2
+
1
a
b
a
c
a
b
b
2
+
1
b
c
a
c
b
c
c
2
+
1
∣
=
1
+
a
2
+
b
2
+
c
2
\begin{vmatrix} a^2 + 1 & ab & ac \\ ab & b^2 + 1 & bc \\ ac & bc & c^2 + 1 \end{vmatrix} = 1 + a^2 + b^2 + c^2
a
2
+
1
ab
a
c
ab
b
2
+
1
b
c
a
c
b
c
c
2
+
1
=
1
+
a
2
+
b
2
+
c
2
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