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1
Romanian District Olympiad 2015, Grade VII, Problem 1
Romanian District Olympiad 2015, Grade VII, Problem 1
Source:
September 25, 2018
arithmetic
Problem Statement
a) Show that the number
9
−
77
⋅
2
⋅
(
11
−
7
)
⋅
(
9
+
77
)
\sqrt{9-\sqrt{77}}\cdot\sqrt {2}\cdot\left(\sqrt{11}-\sqrt{7}\right)\cdot\left( 9+\sqrt{77}\right)
9
−
77
⋅
2
⋅
(
11
−
7
)
⋅
(
9
+
77
)
is natural.b) Consider two real numbers
x
,
y
x,y
x
,
y
such that
x
y
=
6
xy=6
x
y
=
6
and
x
,
y
>
2.
x,y>2.
x
,
y
>
2.
Show that
x
+
y
<
5.
x+y<5.
x
+
y
<
5.
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