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National and Regional Contests
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USA - Middle School Tournaments
Math Invitational for Girls
2020 MIG
8
8
Part of
2020 MIG
Problems
(1)
2020 Individual #8
Source:
4/30/2022
(
1
+
3
)
2
(1 + \sqrt 3)^2
(
1
+
3
)
2
may be written as
a
+
b
3
a + b \sqrt 3
a
+
b
3
for certain integers
a
a
a
and
b
b
b
. What is
a
+
b
a + b
a
+
b
?
<
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p
a
n
c
l
a
s
s
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′
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a
t
e
x
−
b
o
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′
>
(
A
)
<
/
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p
a
n
>
1
<
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p
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n
c
l
a
s
s
=
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x
−
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>
(
B
)
<
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2
<
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c
l
a
s
s
=
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a
t
e
x
−
b
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>
(
C
)
<
/
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a
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>
4
<
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n
c
l
a
s
s
=
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l
a
t
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x
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b
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>
(
D
)
<
/
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>
6
<
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a
s
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>
(
E
)
<
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>
7
<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>4\qquad<span class='latex-bold'>(D) </span>6\qquad<span class='latex-bold'>(E) </span>7
<
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(
A
)
<
/
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>
1
<
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c
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a
ss
=
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a
t
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−
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′
>
(
B
)
<
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>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
6
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
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p
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>
7
2020 Individual