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3
f(x^3+y^3)=f(x^3)+3x^3f(x)f(y)+3f(x)(f(y))^2+y^6f(y)
f(x^3+y^3)=f(x^3)+3x^3f(x)f(y)+3f(x)(f(y))^2+y^6f(y)
Source: 2020 Estonia TST 1.3
November 18, 2020
algebra
functional
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f :R \to R
f
:
R
ā
R
such that for all real numbers
x
x
x
and
y
y
y
f
(
x
3
+
y
3
)
=
f
(
x
3
)
+
3
x
3
f
(
x
)
f
(
y
)
+
3
f
(
x
)
(
f
(
y
)
)
2
+
y
6
f
(
y
)
f(x^3+y^3)=f(x^3)+3x^3f(x)f(y)+3f(x)(f(y))^2+y^6f(y)
f
(
x
3
+
y
3
)
=
f
(
x
3
)
+
3
x
3
f
(
x
)
f
(
y
)
+
3
f
(
x
)
(
f
(
y
)
)
2
+
y
6
f
(
y
)
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