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Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2014 National Olympiad First Round
15
15
Part of
2014 National Olympiad First Round
Problems
(1)
P15 [Algebra] - Turkish NMO 1st Round - 2014
Source:
5/23/2014
What is the sum of distinct real numbers
x
x
x
such that
(
2
x
2
+
5
x
+
9
)
2
=
56
(
x
3
+
1
)
(2x^2+5x+9)^2=56(x^3+1)
(
2
x
2
+
5
x
+
9
)
2
=
56
(
x
3
+
1
)
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
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x
−
b
o
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′
>
(
A
)
<
/
s
p
a
n
>
3
<
s
p
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c
l
a
s
s
=
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>
(
B
)
<
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>
7
4
<
s
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c
l
a
s
s
=
′
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a
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e
x
−
b
o
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′
>
(
C
)
<
/
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a
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>
4
<
s
p
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c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
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′
>
(
D
)
<
/
s
p
a
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>
9
2
<
s
p
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c
l
a
s
s
=
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a
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>
(
E
)
<
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>
None of the preceding
<span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ \dfrac{7}{4} \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ \dfrac{9}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
<
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p
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a
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(
A
)
<
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>
3
<
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a
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=
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a
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x
−
b
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d
′
>
(
B
)
<
/
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>
4
7
<
s
p
an
c
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a
ss
=
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l
a
t
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x
−
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′
>
(
C
)
<
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>
4
<
s
p
an
c
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a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
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p
an
>
2
9
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the preceding