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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2020 Dutch BxMO TST
3
f (x^2y) + 2f (y^2) =(x^2 + f (y)) f (y)
f (x^2y) + 2f (y^2) =(x^2 + f (y)) f (y)
Source: 2020 Dutch BxMO TST p3
November 23, 2020
algebra
functional equation
functional
Problem Statement
Find all functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
that satisfy
f
(
x
2
y
)
+
2
f
(
y
2
)
=
(
x
2
+
f
(
y
)
)
⋅
f
(
y
)
f (x^2y) + 2f (y^2) =(x^2 + f (y)) \cdot f (y)
f
(
x
2
y
)
+
2
f
(
y
2
)
=
(
x
2
+
f
(
y
))
⋅
f
(
y
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
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