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India Pre-Regional Mathematical Olympiad
2016 India PRMO
10
2016 preRMO p10, [M], M is max of (6x-3y-8z) when 2x^2+3y^2+4z^2 = 1
2016 preRMO p10, [M], M is max of (6x-3y-8z) when 2x^2+3y^2+4z^2 = 1
Source:
August 9, 2019
algebra
floor function
maximum
Problem Statement
Let
M
M
M
be the maximum value of
(
6
x
−
3
y
−
8
z
)
(6x-3y-8z)
(
6
x
−
3
y
−
8
z
)
, subject to
2
x
2
+
3
y
2
+
4
z
2
=
1
2x^2+3y^2+4z^2 = 1
2
x
2
+
3
y
2
+
4
z
2
=
1
. Find
[
M
]
[M]
[
M
]
.
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