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2006 Hanoi Open Mathematics Competitions
9
9
Part of
2006 Hanoi Open Mathematics Competitions
Problems
(2)
smallest possible value x^2 + y^2 - x -y - xy (HOMC 2006 J Q9)
Source:
7/23/2019
What is the smallest possible value of
x
2
+
y
2
−
x
−
y
−
x
y
x^2 + y^2 - x -y - xy
x
2
+
y
2
−
x
−
y
−
x
y
?
algebra
minimum
inequalities
Inequalities
Source: HOMC senior 2006
3/9/2016
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
∣
inequalities
algebra
inequalities open