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National and Regional Contests
Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
35
35
Part of
2008 National Olympiad First Round
Problems
(1)
Turkey NMO 2008 1st Round - P35 (Algebra)
Source:
8/27/2012
What is the least real value of the expression
x
2
−
6
x
+
13
+
x
2
−
14
x
+
58
\sqrt{x^2-6x+13} + \sqrt{x^2-14x+58}
x
2
−
6
x
+
13
+
x
2
−
14
x
+
58
where
x
x
x
is a real number?
<
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(
A
)
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39
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(
B
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6
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(
C
)
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43
6
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(
D
)
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2
2
+
13
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>
(
E
)
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None of the above
<span class='latex-bold'>(A)</span>\ \sqrt {39} \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ \frac {43}6 \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt 2 + \sqrt {13} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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A
)
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39
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(
B
)
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6
<
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(
C
)
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6
43
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>
(
D
)
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>
2
2
+
13
<
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a
ss
=
′
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a
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x
−
b
o
l
d
′
>
(
E
)
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/
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>
None of the above