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1988 Greece National Olympiad
1
\sqrt{1987+a}+\sqrt{1987+b}=2\sqrt{1987+c} 1988 Greece MO Grade X p1
\sqrt{1987+a}+\sqrt{1987+b}=2\sqrt{1987+c} 1988 Greece MO Grade X p1
Source:
September 7, 2024
algebra
inequalities
Problem Statement
Let
a
>
0
,
b
>
0
,
c
>
0
a>0,b>0,c>0
a
>
0
,
b
>
0
,
c
>
0
and
1987
+
a
+
1987
+
b
=
2
1987
+
c
\sqrt{1987+a}+\sqrt{1987+b}=2\sqrt{1987+c}
1987
+
a
+
1987
+
b
=
2
1987
+
c
. Prove that
1
2
(
a
+
b
)
≥
c
\frac{1}{2} (a+b )\ge c
2
1
(
a
+
b
)
≥
c
.
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