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Problems
Contests
National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2022 JBMO TST - Turkey
6
6
Part of
2022 JBMO TST - Turkey
Problems
(1)
f(c)f(-c)>=f(a) where f(x)=x^2-2ax+b
Source: 2022 Turkey JBMO TST P6
3/15/2022
Let
c
c
c
be a real number. If the inequality
f
(
c
)
⋅
f
(
−
c
)
≥
f
(
a
)
f(c)\cdot f(-c)\ge f(a)
f
(
c
)
⋅
f
(
−
c
)
≥
f
(
a
)
holds for all
f
(
x
)
=
x
2
−
2
a
x
+
b
f(x)=x^2-2ax+b
f
(
x
)
=
x
2
−
2
a
x
+
b
where
a
a
a
and
b
b
b
are arbitrary real numbers, find all possible values of
c
c
c
.
Inequality
real number