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

$a^{2}+b^{2}=50$
$a=1\Rightarrow b^{2}=49$
$\Rightarrow b=\pm7$
$a=2,3,4,6$ do not give integer value of $b$ .
$a=5\Rightarrow b^{2}=25\Rightarrow b=\pm5$
$a=7\Rightarrow b^{2}=1$
$\Rightarrow b=\pm1$
Similarly,
$a=-1\Rightarrow b=\pm7$
$a=-5\Rightarrow b=\pm5$
$a=-7 \rightarrow b=\pm1$
$\Rightarrow $ The required number of elements $\left(\right.a,b\left.\right)=12$