Question

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

• A. $2$
• B. $4$
• C. $8$
• D. $12$

Answer 1

Answer: (C)

$2a^2+3b^2=35$, $a$, $b\in Z$
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 $8$.