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Junior Tuymaada Olympiad
2006 Junior Tuymaada Olympiad
4
4
Part of
2006 Junior Tuymaada Olympiad
Problems
(1)
1/(x ^ 2+y+z) +1/(x+y^2+z) + 1/(x+y+z^2) <=1, if x+y+z=3, x,y,z >=0
Source: Tuymaada Junior 2006 p4
5/12/2019
The sum of non-negative numbers
x
x
x
,
y
y
y
and
z
z
z
is
3
3
3
. Prove the inequality
1
x
2
+
y
+
z
+
1
x
+
y
2
+
z
+
1
x
+
y
+
z
2
≤
1.
{1 \over x ^ 2 + y + z} + {1 \over x + y ^ 2 + z} + {1 \over x + y + z ^ 2} \leq 1.
x
2
+
y
+
z
1
+
x
+
y
2
+
z
1
+
x
+
y
+
z
2
1
≤
1.
algebra
inequalities
three variable inequality