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2
inf|z²-az+a|
inf|z²-az+a|
Source: Romanian NO, grade x, p.2
October 2, 2019
complex numbers
minima
inequalities
complex disc
Problem Statement
Let be a real number
a
∈
[
2
+
2
,
4
]
.
a\in \left[ 2+\sqrt 2,4 \right] .
a
∈
[
2
+
2
,
4
]
.
Find
inf
∣
z
∣
≤
1
z
∈
C
∣
z
2
−
a
z
+
a
∣
.
\inf_{\stackrel{z\in\mathbb{C}}{|z|\le 1}} \left| z^2-az+a \right| .
in
f
∣
z
∣
≤
1
z
∈
C
z
2
−
a
z
+
a
.
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