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Problems
Contests
International Contests
Tuymaada Olympiad
2021 Tuymaada Olympiad
1
1
Part of
2021 Tuymaada Olympiad
Problems
(2)
Tuymaada 2021/ J1
Source: Tuymaada 2021 / J1
7/30/2021
Quadratic trinomials
F
F
F
and
G
G
G
satisfy
F
(
F
(
x
)
)
>
F
(
G
(
x
)
)
>
G
(
G
(
x
)
)
F(F(x)) > F(G(x)) > G(G(x))
F
(
F
(
x
))
>
F
(
G
(
x
))
>
G
(
G
(
x
))
for all real
x
x
x
. Prove that
F
(
x
)
>
G
(
x
)
F(x) > G(x)
F
(
x
)
>
G
(
x
)
for all real
x
x
x
.
Too Ez polynomial inequality
Source: Tuymaada 2021 Senior P1
7/28/2021
Polynomials
F
F
F
and
G
G
G
satisfy:
F
(
F
(
x
)
)
>
G
(
F
(
x
)
)
>
G
(
G
(
x
)
)
F(F(x))>G(F(x))>G(G(x))
F
(
F
(
x
))
>
G
(
F
(
x
))
>
G
(
G
(
x
))
for all real
x
x
x
.Prove that
F
(
x
)
>
G
(
x
)
F(x)>G(x)
F
(
x
)
>
G
(
x
)
for all real
x
x
x
.
inequalities