MathDB
Problems
Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan IZHO TST
2020 Azerbaijan IZHO TST
5
Hard one ...
Hard one ...
Source: Azerbaijan Math Olympiad Training
December 14, 2019
algebra
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive real numbers such that
x
4
+
y
4
+
z
4
=
1
x^4+y^4+z^4=1
x
4
+
y
4
+
z
4
=
1
. Determine with proof the minimum value of
x
3
1
−
x
8
+
y
3
1
−
y
8
+
z
3
1
−
z
8
\frac{x^3}{1-x^8}+\frac{y^3}{1-y^8}+\frac{z^3}{1-z^8}
1
−
x
8
x
3
+
1
−
y
8
y
3
+
1
−
z
8
z
3
Back to Problems
View on AoPS