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MathLinks Contest 2nd
1.1
1.1
Part of
MathLinks Contest 2nd
Problems
(1)
0211 inequalities 2nd edition Round 1 p1
Source:
5/10/2021
Let
x
,
y
,
z
x, y, z
x
,
y
,
z
be positive numbers such that
x
y
z
≤
2
xyz \le 2
x
yz
≤
2
and
1
x
2
+
1
y
2
+
1
z
2
<
k
\frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2}< k
x
2
1
+
y
2
1
+
z
2
1
<
k
, for some real
k
≥
2
k \ge 2
k
≥
2
. Find all values of
k
k
k
such that the conditions above imply that there exist a triangle having the side-lengths
x
,
y
,
z
x, y, z
x
,
y
,
z
.
inequalities
2nd edition