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2017 Pan African
Problem 2
Problem 2
Part of
2017 Pan African
Problems
(1)
Inequality x^2y+y^2z+z^2x \geq 2(x+y+z)-3 [PAMO 2017, P2]
Source: Pan African Mathematical Olympiad 2017, Problem 2
7/5/2017
Let
x
,
y
x,y
x
,
y
, and
z
z
z
be positive real numbers such that
x
y
+
y
z
+
z
x
=
3
x
y
z
xy+yz+zx=3xyz
x
y
+
yz
+
z
x
=
3
x
yz
. Prove that
x
2
y
+
y
2
z
+
z
2
x
≥
2
(
x
+
y
+
z
)
−
3.
x^2y+y^2z+z^2x \geq 2(x+y+z)-3.
x
2
y
+
y
2
z
+
z
2
x
≥
2
(
x
+
y
+
z
)
−
3.
In which cases do we have equality?
algebraic inequality
PAMO
inequalities