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Soros Olympiad in Mathematics
II Soros Olympiad 1995 - 96 (Russia)
10.1
a^2x^2 + y^2 + z^2 >= ayz+xy+xz (II Soros Olympiad 1995-96 R1 10.1)
a^2x^2 + y^2 + z^2 >= ayz+xy+xz (II Soros Olympiad 1995-96 R1 10.1)
Source:
June 3, 2024
inequalities
algebra
Problem Statement
Find all values of
a
a
a
for which the inequality
a
2
x
2
+
y
2
+
z
2
≥
a
y
z
+
x
y
+
x
z
a^2x^2 + y^2 + z^2 \ge ayz+xy+xz
a
2
x
2
+
y
2
+
z
2
≥
a
yz
+
x
y
+
x
z
holds for all
x
x
x
,
y
y
y
and
z
z
z
.
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