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National and Regional Contests
Turkey Contests
National Olympiad First Round
2004 National Olympiad First Round
28
28
Part of
2004 National Olympiad First Round
Problems
(1)
P28 [Algebra] - Turkish NMO 1st Round - 2004
Source:
11/16/2013
What is the largest possible value of
8
x
2
+
9
x
y
+
18
y
2
+
2
x
+
3
y
8x^2+9xy+18y^2+2x+3y
8
x
2
+
9
x
y
+
18
y
2
+
2
x
+
3
y
such that
4
x
2
+
9
y
2
=
8
4x^2 + 9y^2 = 8
4
x
2
+
9
y
2
=
8
where
x
,
y
x,y
x
,
y
are real numbers?
<
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23
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26
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29
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D
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31
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35
<span class='latex-bold'>(A)</span>\ 23 \qquad<span class='latex-bold'>(B)</span>\ 26 \qquad<span class='latex-bold'>(C)</span>\ 29 \qquad<span class='latex-bold'>(D)</span>\ 31 \qquad<span class='latex-bold'>(E)</span>\ 35
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(
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>
23
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>
(
B
)
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>
26
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−
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′
>
(
C
)
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>
29
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−
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d
′
>
(
D
)
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p
an
>
31
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=
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a
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x
−
b
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d
′
>
(
E
)
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>
35