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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2019 India PRMO
2
Simple Function Solving
Simple Function Solving
Source:
August 11, 2019
function
functions
Problem Statement
Ket
f
(
x
)
=
x
2
+
a
x
+
b
f(x) = x^{2} +ax + b
f
(
x
)
=
x
2
+
a
x
+
b
. If for all nonzero real
x
x
x
f
(
x
+
1
x
)
=
f
(
x
)
+
f
(
1
x
)
f\left(x + \dfrac{1}{x}\right) = f\left(x\right) + f\left(\dfrac{1}{x}\right)
f
(
x
+
x
1
)
=
f
(
x
)
+
f
(
x
1
)
and the roots of
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
are integers, what is the value of
a
2
+
b
2
a^{2}+b^{2}
a
2
+
b
2
?
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