Question

The number of elements in the set $\left\{\left(a,b\right):a^2+b^2=50;a,b\in Z\right\}$ , where $Z$ is the set of all integers, is

Answer 1

Answer: 12

$a^2+b^2=50$
$a=1\Rightarrow b^2=49$
$\Rightarrow b=\pm 7$
$a=2,3,4,6$ do not give integer value of $b$ .
$a=5\Rightarrow b^2=25\Rightarrow b=\pm 5$
$a=7\Rightarrow b^2=1$
$\Rightarrow b=\pm 1$
Similarly,
$a=-1\Rightarrow b=\pm 7$
$a=-5\Rightarrow b=\pm 5$
$a=-7\to b=\pm 1$
$\Rightarrow$ The required number of elements $(a,b)=12$