MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2006 Hanoi Open Mathematics Competitions
9
Inequalities
Inequalities
Source: HOMC senior 2006
March 9, 2016
inequalities
algebra
inequalities open
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be real numbers such that
x
2
+
y
2
+
z
2
=
1
x^2+y^2+z^2=1
x
2
+
y
2
+
z
2
=
1
.Find the largest posible value of
∣
x
3
+
y
3
+
z
3
−
x
y
z
∣
|x^3+y^3+z^3-xyz|
∣
x
3
+
y
3
+
z
3
−
x
yz
∣
Back to Problems
View on AoPS