The number of elements in the relation R=(x,y):4x^2+y^2

Question

The number of elements in the relation $R={(x,y):4{x}^{2}+{y}^{2}<52,x,y\in Z}$ is

Accepted Answer

$\begin{gathered} \underset{\, \, \, \, \, \downarrow }{4}{x}^{2}+{y}_{2}^{\downarrow }<52,x,y\in Z \ 0\, 0,\pm 1,\pm 2,\pm 3,\pm 4,\pm 5,\pm 6,\pm 7	o 1	imes 15=15 \ \pm 1\, 0,\pm 1,\pm 2,\pm 3\ldots \ldots \ldots .\pm 6	o 2	imes 13=26 \ +2\, 0,\pm 1\pm 2\pm 3\ldots \ldots \ldots .\pm 5	o 2	imes 11=22 \ \pm 3\, 0,\pm 1,\pm 2,\pm 3	o 2	imes 7=14 \ =77 \end{gathered}$

Solutions · 1