MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2010 National Olympiad First Round
35
35
Part of
2010 National Olympiad First Round
Problems
(1)
Turkey NMO 2010 1st Round - P35 (Algebra)
Source:
7/27/2012
Which one below is not less than
x
3
+
y
5
x^3+y^5
x
3
+
y
5
for all reals
x
,
y
x,y
x
,
y
such that
0
<
x
<
1
0<x<1
0
<
x
<
1
and
0
<
y
<
1
0<y<1
0
<
y
<
1
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
x
2
y
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
x
2
y
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
x
2
y
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
x
3
y
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
x
y
4
<span class='latex-bold'>(A)</span>\ x^2y \qquad<span class='latex-bold'>(B)</span>\ x^2y^2 \qquad<span class='latex-bold'>(C)</span>\ x^2y^3 \qquad<span class='latex-bold'>(D)</span>\ x^3y \qquad<span class='latex-bold'>(E)</span>\ xy^4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
x
2
y
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
x
2
y
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
x
2
y
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
x
3
y
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
x
y
4