MathDB
Problems
Contests
National and Regional Contests
Cuba Contests
Cuba MO
2011 Cuba MO
5
f(x)f(y) = 2f(x + y) + 9xy
f(x)f(y) = 2f(x + y) + 9xy
Source: 2011 Cuba MO 2.5
September 17, 2024
algebra
functional
functional equation
Problem Statement
Determine all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
)
f
(
y
)
=
2
f
(
x
+
y
)
+
9
x
y
∀
x
,
y
∈
R
.
f(x)f(y) = 2f(x + y) + 9xy \ \ \forall x, y \in R.
f
(
x
)
f
(
y
)
=
2
f
(
x
+
y
)
+
9
x
y
∀
x
,
y
∈
R
.
Back to Problems
View on AoPS