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2012 Hanoi Open Mathematics Competitions
15
Q15 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Q15 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Source:
June 10, 2012
Problem Statement
Q15. Determine the greatest value of the sum
M
=
x
y
+
y
z
+
z
x
M=xy+yz+zx
M
=
x
y
+
yz
+
z
x
, where
x
,
y
,
z
x,y,z
x
,
y
,
z
are real numbers satisfying the following condition
x
2
+
2
y
2
+
5
z
2
=
22.
x^2+2y^2+5z^2=22.
x
2
+
2
y
2
+
5
z
2
=
22.
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