First slide

Operations on Sets

Question

$The number of elements in the set \{(a, b) : 2 a^{2} + 3 b^{2} = 35, a, b \in Z}, where Z is the set of all integers, is$

Moderate

A

2
B

4
C

8
D

12

Solution

$Given set is \{(a, b) : 2 a^{2} + 3 b^{2} = 35, a, b \in Z\}$
$We can see that, 2 (\pm 2)^{2} + 3 (\pm 3)^{2} = 35 and 2 (\pm 4)^{2} + 3 (\pm 1)^{2} = 35$
$∴ (2, 3), (2, - 3), (- 2, - 3), (- 2, 3), (4, 1), (4, - 1), (- 4, - 1), (- 4, 1)$
$eight elements of the set, so n = 8 .$

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