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Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
11.2
max C: (x + y +z + u)^2 >= Cyz (V Soros Olympiad 1998-99 Round 1 11.2)
max C: (x + y +z + u)^2 >= Cyz (V Soros Olympiad 1998-99 Round 1 11.2)
Source:
May 25, 2024
algebra
inequalities
Problem Statement
Find the greatest value of
C
C
C
for which, for any
x
,
y
,
z
,
u
x, y, z,u
x
,
y
,
z
,
u
, and such that for
0
≤
x
≤
y
≤
z
≤
u
0\le x\le y \le z\le u
0
≤
x
≤
y
≤
z
≤
u
, holds the inequality
(
x
+
y
+
z
+
u
)
2
≥
C
y
z
.
(x + y +z + u)^2 \ge Cyz .
(
x
+
y
+
z
+
u
)
2
≥
C
yz
.
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