Answer
$-1$ $,$ $0$ $,$ $\dfrac{2}{3}$ $,$ $\dfrac{5}{6}$ and $1$ satisfy the inequality
Work Step by Step
$x^{2}+2\lt4$ $;$ $S=\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\}$
$x=-5$
$(-5)^{2}+2\lt4$
$25+2\lt4$
$27\lt4$ False
$x=-1$
$(-1)^{2}+2\lt4$
$1+2\lt4$
$3\lt4$ True
$x=0$
$(0)^{2}+2\lt4$
$2\lt4$ True
$x=\dfrac{2}{3}$
$\Big(\dfrac{2}{3}\Big)^{2}+2\lt4$
$\dfrac{4}{9}+2\lt4$
$\dfrac{22}{9}\lt4$
$2.44\lt4$ True
$x=\dfrac{5}{6}$
$\Big(\dfrac{5}{6}\Big)^{2}+2\lt4$
$\dfrac{25}{36}+2\lt4$
$\dfrac{97}{36}\lt4$
$2.694\lt4$ True
$x=1$
$(1)^{2}+2\lt4$
$1+2\lt4$
$3\lt4$ True
$x=\sqrt{5}$
$(\sqrt{5})^{2}+2\lt4$
$5+2\lt4$
$7\lt4$ False
$x=3$
$3^{2}+2\lt4$
$9+2\lt4$
$11\lt4$ False
$x=5$
$5^{2}+2\lt4$
$25+2\lt4$
$27\lt4$ False
