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Q.
The number of elements in the set $\{(a, b)$ : $2a^2 + 3b^2 = 35$, $a, b \in Z\}$, where $Z$ is the set of all integers, is
Relations and Functions
Solution:
$2a^2 + 3b^2 = 35$, $a$, $b \in Z$
If $a = 2$, $b = 3$, then $2 \times 2^2 + 3 \times 3^2 = 35$
$\therefore (a, b)$ 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 $8$.