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2013 Turkey Junior National Olympiad
1
1
Part of
2013 Turkey Junior National Olympiad
Problems
(1)
Find max of |(x-y)(y-z)(z-x)|
Source: Turkey Junior National Olympiad 2013 P1
11/29/2013
Let
x
,
y
,
z
x, y, z
x
,
y
,
z
be real numbers satisfying
x
+
y
+
z
=
0
x+y+z=0
x
+
y
+
z
=
0
and
x
2
+
y
2
+
z
2
=
6
x^2+y^2+z^2=6
x
2
+
y
2
+
z
2
=
6
. Find the maximum value of
∣
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
∣
|(x-y)(y-z)(z-x) |
∣
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
∣
inequalities
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