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Turkey Contests
Turkey Junior National Olympiad
2021 Turkey Junior National Olympiad
3
3
Part of
2021 Turkey Junior National Olympiad
Problems
(1)
max x-y where Σx=2 and Σxy=1
Source: Turkey Junior National Olympiad 2021 P3
1/7/2022
Let
x
,
y
,
z
x, y, z
x
,
y
,
z
be real numbers such that
x
+
y
+
z
=
2
,
x
y
+
y
z
+
z
x
=
1
x+y+z=2, \;\;\;\; xy+yz+zx=1
x
+
y
+
z
=
2
,
x
y
+
yz
+
z
x
=
1
Find the maximum possible value of
x
−
y
x-y
x
−
y
.
inequalities
maximum value
Find maximum