Question

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

• A. $2$
• B. $4$
• C. $8$
• D. $12$

Answer 1

The correct option is C $8$

Let $2x+3y=35,x,y>0$

Integral solution $\Rightarrow (a^2=x,y^2=b^2)$

$\therefore (a^2,b^2)=(4,a)$ and $(16,1)$

$\therefore (a,b)\cong (2,3),(-2,-3),(2,-3),(-2,3),(4,1),(-4,-1),(-4,1),(4,-1)$

$\therefore 8$ elements $\Rightarrow \left(C\right)$