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Problem
Problem
If
x
2
+
y
2
+
z
2
=
1
x^2 + y^2 + z^2 = 1
x
2
+
y
2
+
z
2
=
1
for
x
,
y
,
z
∈
R
x, y, z \in \mathbb{R}
x
,
y
,
z
∈
R
, then the maximum value of
x
3
+
y
3
+
z
3
−
3
x
y
z
x^3 + y^3 + z^3 - 3xyz
x
3
+
y
3
+
z
3
−
3
x
y
z
is a.
1
2
\frac{1}{2}
2
1
b. 1 c. 2 d. 3
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