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2017-IMOC
A1
A1
Part of
2017-IMOC
Problems
(1)
(a^n+1)(b^n+1)>=4 if a+b=2
Source: IMOC 2017 A1
8/12/2021
Prove that for all
a
,
b
>
0
a,b>0
a
,
b
>
0
with
a
+
b
=
2
a+b=2
a
+
b
=
2
, we have
(
a
n
+
1
)
(
b
n
+
1
)
≥
4
\left(a^n+1\right)\left(b^n+1\right)\ge4
(
a
n
+
1
)
(
b
n
+
1
)
≥
4
for all
n
∈
N
≥
2
n\in\mathbb N_{\ge2}
n
∈
N
≥
2
.
inequalities
algebra