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. $8$
• C. $4$
• D. $12$

Answer 1

Answer: (B)

$8$

$(a,b):2a^2+3b^2=35,a,b\in Z$
$⟹2(\pm 2{)}^2+3(\pm 3{)}^2=35$ and $2(\pm 4{)}^2+3(\pm 1{)}^2=35$
$\therefore (a,b)=(2,3),(2,-3),(-2,-3),(-2,3),(4,1),(4,-1),(-4,-1),(-4,1)$

i.e. $8$ elements