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National and Regional Contests
China Contests
XES Mathematics Olympiad
the 13th XMO
P9
two variable inequality
two variable inequality
Source:
June 18, 2023
inequalities
algebra
Problem Statement
Find the maximum value of
λ
,
\lambda ,
λ
,
such that for
∀
x
,
y
∈
R
+
\forall x,y\in\mathbb R_+
∀
x
,
y
∈
R
+
satisfying
2
x
−
y
=
2
x
3
+
y
3
,
x
2
+
λ
y
2
⩽
1.
2x-y=2x^3+y^3,x^2+\lambda y^2\leqslant 1.
2
x
−
y
=
2
x
3
+
y
3
,
x
2
+
λ
y
2
⩽
1.
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