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Korea Junior Mathematics Olympiad
2004 Korea Junior Math Olympiad
1
1
Part of
2004 Korea Junior Math Olympiad
Problems
(1)
Inscribing five squares
Source: 2004 Korea Junior Math Olympiad
6/28/2024
For positive reals
a
1
,
a
2
,
.
.
.
,
a
5
a_1, a_2, ..., a_5
a
1
,
a
2
,
...
,
a
5
such that
a
1
2
+
a
2
2
+
.
.
.
+
a
5
2
=
2
a^2_1+a^2_2+...+a^2_5=2
a
1
2
+
a
2
2
+
...
+
a
5
2
=
2
, consider five squares with sides
a
1
,
a
2
,
.
.
.
,
a
5
a_1, a_2, ..., a_5
a
1
,
a
2
,
...
,
a
5
respectively. Show that these squares can be placed inside (including boundaries) a square with side length of
2
2
2
so that the square themselves do not overlap each other.
geometry
KMO
inequalities