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2009 Kyrgyzstan National Olympiad
3
If f(x^2 +x +3) +2*f(x^2 - 3x + 5) = 6x^2 - 10x +17, find f(2009)
If f(x^2 +x +3) +2*f(x^2 - 3x + 5) = 6x^2 - 10x +17, find f(2009)
Source: KG National 2009
April 23, 2009
function
algebra
polynomial
algebra unsolved
Problem Statement
For function
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
given that
f
(
x
2
+
x
+
3
)
+
2
⋅
f
(
x
2
−
3
x
+
5
)
=
6
x
2
−
10
x
+
17
f(x^2 +x +3) +2 \cdot f(x^2 - 3x + 5) = 6x^2 - 10x +17
f
(
x
2
+
x
+
3
)
+
2
⋅
f
(
x
2
−
3
x
+
5
)
=
6
x
2
−
10
x
+
17
, calculate
f
(
2009
)
f(2009)
f
(
2009
)
.
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