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Romania National Olympiad
2011 Romania National Olympiad
1
x + y + z<=t,, x^2 + y^2 + z^2>=t , x^3 + y^3 + z^3<=t 2011 Romania NMO VIII p1
x + y + z<=t,, x^2 + y^2 + z^2>=t , x^3 + y^3 + z^3<=t 2011 Romania NMO VIII p1
Source:
August 15, 2024
algebra
inequalities
Problem Statement
Find all real numbers
x
,
y
,
z
,
t
∈
[
0
,
∞
)
x, y,z,t \in [0, \infty)
x
,
y
,
z
,
t
∈
[
0
,
∞
)
so that
x
+
y
+
z
≤
t
,
x
2
+
y
2
+
z
2
≥
t
a
n
d
x
3
+
y
3
+
z
3
≤
t
.
x + y + z \le t, \,\,\, x^2 + y^2 + z^2 \ge t \,\,\, and \,\,\,x^3 + y^3 + z^3 \le t.
x
+
y
+
z
≤
t
,
x
2
+
y
2
+
z
2
≥
t
an
d
x
3
+
y
3
+
z
3
≤
t
.
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