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China Team Selection Test
2019 China Team Selection Test
1
Inequality about complex numbers
Inequality about complex numbers
Source: 2019 China TST Test 3 P1
March 23, 2019
inequalities
complex numbers
algebra
China
China TST
Problem Statement
Given complex numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
, with
∣
x
∣
2
+
∣
y
∣
2
+
∣
z
∣
2
=
1
|x|^2+|y|^2+|z|^2=1
∣
x
∣
2
+
∣
y
∣
2
+
∣
z
∣
2
=
1
. Prove that:
∣
x
3
+
y
3
+
z
3
−
3
x
y
z
∣
≤
1
|x^3+y^3+z^3-3xyz| \le 1
∣
x
3
+
y
3
+
z
3
−
3
x
yz
∣
≤
1
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