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National Olympiad First Round
2000 National Olympiad First Round
4
Turkey NMO 2000 1st Round - P04 (Algebra)
Turkey NMO 2000 1st Round - P04 (Algebra)
Source:
July 24, 2012
Problem Statement
What is the sum of real roots of
(
x
x
)
x
=
x
x
x
(x\sqrt{x})^x = x^{x\sqrt{x}}
(
x
x
)
x
=
x
x
x
?
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(
A
)
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a
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>
18
7
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B
)
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a
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>
71
4
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a
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(
C
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9
4
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s
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a
t
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x
−
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>
(
D
)
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>
24
19
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(
E
)
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13
4
<span class='latex-bold'>(A)</span>\ \frac{18}{7} \qquad<span class='latex-bold'>(B)</span>\ \frac{71}{4} \qquad<span class='latex-bold'>(C)</span>\ \frac{9}{4} \qquad<span class='latex-bold'>(D)</span>\ \frac{24}{19} \qquad<span class='latex-bold'>(E)</span>\ \frac{13}{4}
<
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x
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(
A
)
<
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an
>
7
18
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c
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l
a
t
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x
−
b
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d
′
>
(
B
)
<
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an
>
4
71
<
s
p
an
c
l
a
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l
a
t
e
x
−
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o
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>
(
C
)
<
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an
>
4
9
<
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p
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c
l
a
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l
a
t
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x
−
b
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d
′
>
(
D
)
<
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an
>
19
24
<
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a
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l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
4
13
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