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Problem
Problem
If the expression
a
x
2
+
b
y
2
+
c
z
2
+
2
a
y
z
+
2
b
x
z
+
2
c
x
y
ax^2 + by^2 + cz^2 + 2ayz + 2bxz + 2cxy
a
x
2
+
b
y
2
+
c
z
2
+
2
a
y
z
+
2
b
x
z
+
2
c
x
y
can be resolved into two rational factors, prove that
a
3
+
b
3
+
c
3
=
3
a
b
c
.
a^3 + b^3 + c^3 = 3abc.
a
3
+
b
3
+
c
3
=
3
ab
c
.
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