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2023-IMOC
A3
A3
Part of
2023-IMOC
Problems
(1)
why is RHS so large
Source: 2023 IMOC A3
9/17/2023
Given positive reals
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfying
x
+
y
+
z
=
3
x+y+z=3
x
+
y
+
z
=
3
, prove that
∑
c
y
c
(
x
2
+
y
2
+
x
2
y
2
+
y
2
x
2
)
≥
4
∑
c
y
c
y
x
.
\sum_{cyc}\left( x^2+y^2+x^2y^2+\frac{y^2}{x^2}\right)\geq 4\sum_{cyc}\frac{y}{x}.
cyc
∑
(
x
2
+
y
2
+
x
2
y
2
+
x
2
y
2
)
≥
4
cyc
∑
x
y
.
Proposed by chengbilly.
inequalities
algebra