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Mathematics
Mathematics
Problem
Let
α
,
β
,
γ
,
δ
∈
Z
\alpha, \beta, \gamma, \delta \in \mathbb{Z}
α
,
β
,
γ
,
δ
∈
Z
and let
A
(
α
,
β
)
A(\alpha, \beta)
A
(
α
,
β
)
,
B
(
1
,
0
)
B(1, 0)
B
(
1
,
0
)
,
C
(
γ
,
δ
)
C(\gamma, \delta)
C
(
γ
,
δ
)
and
D
(
1
,
2
)
D(1, 2)
D
(
1
,
2
)
be the vertices of a parallelogram
A
B
C
D
ABCD
A
B
C
D
. If
A
B
=
10
AB = \sqrt{10}
A
B
=
10
and the points
A
A
A
and
C
C
C
lie on the line
3
y
=
2
x
+
1
3y = 2x + 1
3
y
=
2
x
+
1
, then
2
(
α
+
β
+
γ
+
δ
)
2(\alpha + \beta + \gamma + \delta)
2
(
α
+
β
+
γ
+
δ
)
is equal to: 10 5 12 8
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