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Problems
Contests
International Contests
Silk Road
2006 Silk Road
1
1
Part of
2006 Silk Road
Problems
(1)
Find all functions f with f(x^2+xy+f(y))=f^2(x)+xf(y)+y
Source: International competition SRMC 2006 P-1
9/8/2010
Found all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
, such that for any
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
,
f
(
x
2
+
x
y
+
f
(
y
)
)
=
f
2
(
x
)
+
x
f
(
y
)
+
y
.
f(x^2+xy+f(y))=f^2(x)+xf(y)+y.
f
(
x
2
+
x
y
+
f
(
y
))
=
f
2
(
x
)
+
x
f
(
y
)
+
y
.
function
algebra solved
algebra