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Tuymaada Olympiad
2002 Tuymaada Olympiad
5
5(x^2+ y^2) ^2 \leq 4 + (x +y) ^4 for x,y in [0,1]
5(x^2+ y^2) ^2 \leq 4 + (x +y) ^4 for x,y in [0,1]
Source: Tuymaada Junior 2002 p5
May 11, 2019
algebra
inequalities
Problem Statement
Prove that for all
x
,
y
∈
x, y \in
x
,
y
∈
0
,
1
0, 1
0
,
1
the inequality
5
(
x
2
+
y
2
)
2
≤
4
+
(
x
+
y
)
4
5 (x^2+ y^2) ^2 \leq 4 + (x +y) ^4
5
(
x
2
+
y
2
)
2
≤
4
+
(
x
+
y
)
4
holds.
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