MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
1990 Greece National Olympiad
3
y^2f(x)(f(x)-2x)\le (1-xy)(1+xy)
y^2f(x)(f(x)-2x)\le (1-xy)(1+xy)
Source: 1990 Greece MO Grade XII p3
September 6, 2024
function
algebra
inequalities
functional
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R}\to\mathbb{R}
f
:
R
→
R
that satisfy
y
2
f
(
x
)
(
f
(
x
)
−
2
x
)
≤
(
1
−
x
y
)
(
1
+
x
y
)
y^2f(x)(f(x)-2x)\le (1-xy)(1+xy)
y
2
f
(
x
)
(
f
(
x
)
−
2
x
)
≤
(
1
−
x
y
)
(
1
+
x
y
)
for any
x
,
y
∈
R
x,y \in\mathbb{R}
x
,
y
∈
R
.
Back to Problems
View on AoPS