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National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2012 Hanoi Open Mathematics Competitions
1
1
Part of
2012 Hanoi Open Mathematics Competitions
Problems
(2)
Q1 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Source:
6/10/2012
Q1. Assum that
a
−
b
=
−
(
a
−
b
)
.
a-b=-(a-b).
a
−
b
=
−
(
a
−
b
)
.
Then:
(
A
)
a
=
b
;
(
B
)
a
<
b
;
(
C
)
a
>
b
(
D
)
It is impossible to compare those of a and b.
(A) \; a=b; \qquad (B) \; a<b; \qquad (C) \; a>b \qquad (D) \; \text{ It is impossible to compare those of a and b.}
(
A
)
a
=
b
;
(
B
)
a
<
b
;
(
C
)
a
>
b
(
D
)
It is impossible to compare those of a and b.
H=(1+x^5-x^7)^{{2012}^{3^{11}}} (HOMC 2012 Q1)
Source:
7/24/2019
Let
x
=
6
+
2
5
+
6
−
2
5
20
x=\frac{\sqrt{6+2\sqrt5}+\sqrt{6-2\sqrt5}}{\sqrt{20}}
x
=
20
6
+
2
5
+
6
−
2
5
. The value of
H
=
(
1
+
x
5
−
x
7
)
2012
3
11
H=(1+x^5-x^7)^{{2012}^{3^{11}}}
H
=
(
1
+
x
5
−
x
7
)
2012
3
11
is (A)
1
1
1
(B)
11
11
11
(C)
21
21
21
(D)
101
101
101
(E) None of the above
algebra