MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2020 Latvia Baltic Way TST
2
2
Part of
2020 Latvia Baltic Way TST
Problems
(1)
Asymmetric FE over reals
Source: Latvian TST for Baltic Way 2020 P2
10/17/2020
Determine all functions
f
:
R
ā
R
f:\mathbb R\to\mathbb R
f
:
R
ā
R
that satisfy equation:
f
(
x
3
+
y
3
)
=
f
(
x
3
)
+
3
x
2
f
(
x
)
f
(
y
)
+
3
f
(
x
)
f
(
y
)
2
+
y
6
f
(
y
)
f(x^3+y^3) =f(x^3) + 3x^2f(x)f(y) + 3f(x)f(y)^2 + y^6f(y)
f
(
x
3
+
y
3
)
=
f
(
x
3
)
+
3
x
2
f
(
x
)
f
(
y
)
+
3
f
(
x
)
f
(
y
)
2
+
y
6
f
(
y
)
for all reals
x
,
y
x,y
x
,
y
function
Functional equation in R
algebra