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Question
Mathematics
The number of elements in the set (a, b): 2a2 + 3b2 = 35, a, b ∈ Z where Z is the set of all integers, is
Q. The number of elements in the set
{(
a
,
b
)
:
2
a
2
+
3
b
2
=
35
,
a
,
b
∈
Z
}
, where
Z
is the set of all integers, is
1976
194
Relations and Functions
Report Error
A
2
9%
B
4
16%
C
8
66%
D
12
9%
Solution:
2
a
2
+
3
b
2
=
35
,
a
,
b
∈
Z
If
a
=
2
,
b
=
3
, then
2
×
2
2
+
3
×
3
2
=
35
∴
(
a
,
b
)
is
(
2
,
3
)
. In the same way, other sets are
(
−
2
,
−
3
)
,
(
4
,
1
)
,
(
−
4
,
−
1
)
,
(
2
,
−
3
)
,
(
−
2
,
3
)
,
(
−
4
,
1
)
,
(
4
,
−
1
)
So, number of elements in the set is
8
.