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EGMO
2014 EGMO
6
6
Part of
2014 EGMO
Problems
(1)
Function related to (x+y)^2
Source: European Girls’ Mathematical Olympiad-2014 - Day 2 - P6
4/13/2014
Determine all functions
f
:
R
→
R
f:\mathbb R\rightarrow\mathbb R
f
:
R
→
R
satisfying the condition
f
(
y
2
+
2
x
f
(
y
)
+
f
(
x
)
2
)
=
(
y
+
f
(
x
)
)
(
x
+
f
(
y
)
)
f(y^2+2xf(y)+f(x)^2)=(y+f(x))(x+f(y))
f
(
y
2
+
2
x
f
(
y
)
+
f
(
x
)
2
)
=
(
y
+
f
(
x
))
(
x
+
f
(
y
))
for all real numbers
x
x
x
and
y
y
y
.
function
quadratics
algebra
functional equation
EGMO
EGMO 2014