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2012 Argentina National Olympiad
1
1
Part of
2012 Argentina National Olympiad
Problems
(1)
min and max of z if x+y+z=7 and xy+yz+zx=11
Source: 2012 Argentina OMA Finals L3 p1
1/15/2023
Determine if there are triplets (
x
,
y
,
z
)
x,y,z)
x
,
y
,
z
)
of real numbers such that
{
x
+
y
+
z
=
7
x
y
+
y
z
+
z
x
=
11
\begin{cases} x+y+z=7 \\ xy+yz+zx=11\end{cases}
{
x
+
y
+
z
=
7
x
y
+
yz
+
z
x
=
11
If the answer is affirmative, find the minimum and maximum values of
z
z
z
in such a triplet.
algebra
system of equations
inequalities
System