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6(x^3+y^3+z^3)^2<=(x^2+y^2+z^2)^3 OLCOMA Costa Rica Finals 2013 SL A1 d1
6(x^3+y^3+z^3)^2<=(x^2+y^2+z^2)^3 OLCOMA Costa Rica Finals 2013 SL A1 d1
Source:
September 26, 2021
algebra
inequalities
Problem Statement
Let the real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
be such that
x
+
y
+
z
=
0
x + y + z = 0
x
+
y
+
z
=
0
. Prove that
6
(
x
3
+
y
3
+
z
3
)
2
≤
(
x
2
+
y
2
+
z
2
)
3
.
6(x^3 + y^3 + z^3)^2 \le (x^2 + y^2 + z^2)^3.
6
(
x
3
+
y
3
+
z
3
)
2
≤
(
x
2
+
y
2
+
z
2
)
3
.
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