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5
Very easy functional equation
Very easy functional equation
Source: 2017 Moldova TST, day 2, problem 1.
March 19, 2017
Problem Statement
Find all continuous functions
f
:
R
→
R
f : R \rightarrow R
f
:
R
→
R
such, that
f
(
x
y
)
=
f
(
x
2
+
y
2
2
)
+
(
x
−
y
)
2
f(xy)= f\left(\frac{x^2+y^2}{2}\right)+(x-y)^2
f
(
x
y
)
=
f
(
2
x
2
+
y
2
)
+
(
x
−
y
)
2
for any real numbers
x
x
x
and
y
y
y
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