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Problems
Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan Junior National Olympiad
2017 Azerbaijan Junior National Olympiad
P3
P3
Part of
2017 Azerbaijan Junior National Olympiad
Problems
(1)
ASU 543 All Soviet Union MO 1991 (x+y+z)^2/3>=x\sqrt{yz}+y\sqrt{zx}+z\sqrt{xy}
Source:
8/14/2019
Show that
(
x
+
y
+
z
)
2
3
≥
x
y
z
+
y
z
x
+
z
x
y
\frac{(x + y + z)^2}{3} \ge x\sqrt{yz} + y\sqrt{zx} + z\sqrt{xy}
3
(
x
+
y
+
z
)
2
≥
x
yz
+
y
z
x
+
z
x
y
for all non-negative reals
x
,
y
,
z
x, y, z
x
,
y
,
z
.
algebra
inequalities