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9
Functional equation
Functional equation
Source: Ukraine TST 2013
June 5, 2013
function
algebra proposed
algebra
Problem Statement
Determine all functions
f
:
R
→
R
f:\Bbb{R}\to\Bbb{R}
f
:
R
→
R
such that
f
2
(
x
+
y
)
=
f
2
(
x
)
+
2
f
(
x
y
)
+
f
2
(
y
)
,
f^2(x+y)=f^2(x)+2f(xy)+f^2(y),
f
2
(
x
+
y
)
=
f
2
(
x
)
+
2
f
(
x
y
)
+
f
2
(
y
)
,
for all
x
,
y
∈
R
.
x,y\in \Bbb{R}.
x
,
y
∈
R
.
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