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Lithuania Contests
Lithuania National Olympiad
2010 Lithuania National Olympiad
1
1
Part of
2010 Lithuania National Olympiad
Problems
(2)
an ineq with 2 variables
Source: Lithuania NMO,2010
3/11/2012
Let
a
,
b
a,b
a
,
b
be real numbers. Prove the inequality
2
(
a
4
+
a
2
b
2
+
b
4
)
≥
3
(
a
3
b
+
a
b
3
)
.
2(a^4+a^2b^2+b^4)\ge 3(a^3b+ab^3).
2
(
a
4
+
a
2
b
2
+
b
4
)
≥
3
(
a
3
b
+
a
b
3
)
.
inequalities
inequalities proposed
the range of a+b
Source: Lithuania NMO 2010
3/11/2012
a
,
b
a,b
a
,
b
are real numbers such that:
a
3
+
b
3
=
8
−
6
a
b
.
a^3+b^3=8-6ab.
a
3
+
b
3
=
8
−
6
ab
.
Find the maximal and minimal value of
a
+
b
a+b
a
+
b
.
inequalities proposed
inequalities