MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAJMO
2016 USAJMO
6
Familiar Solution Set
Familiar Solution Set
Source: JMO/6, USAMO/4 2016
April 20, 2016
USAJMO
USA(J)MO
2016 USAJMO
2016 USAJMO Problem 6
function
algebra
Hi
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that for all real numbers
x
x
x
and
y
y
y
,
(
f
(
x
)
+
x
y
)
⋅
f
(
x
−
3
y
)
+
(
f
(
y
)
+
x
y
)
⋅
f
(
3
x
−
y
)
=
(
f
(
x
+
y
)
)
2
.
(f(x)+xy)\cdot f(x-3y)+(f(y)+xy)\cdot f(3x-y)=(f(x+y))^2.
(
f
(
x
)
+
x
y
)
⋅
f
(
x
−
3
y
)
+
(
f
(
y
)
+
x
y
)
⋅
f
(
3
x
−
y
)
=
(
f
(
x
+
y
)
)
2
.
Back to Problems
View on AoPS