Answer:Option (2) is correct.s = 7 satisfy the given equation [tex]s=4+\sqrt{s+2}[/tex].Step-by-step explanation:Consider the given equation,[tex]s=4+\sqrt{s+2}[/tex] We have to solve for the value of s so that it satisfy the given equationWe first check for s = 2,LHS = s = 2RHS = [tex]4+\sqrt{s+2}[/tex] Put s = 2 , we get ,[tex]s=4+\sqrt{2+2}=4+\sqrt{4}=4+2=6[/tex]we get LHS = 2 and RHS = 6 which are not equal.Thus, s = 2 does not satisy the given equation.We now check for s = 7 LHS = s = 7RHS = [tex]4+\sqrt{s+2}[/tex] Put s = 7 , we get ,[tex]s=4+\sqrt{7+2}=4+\sqrt{9}=4+3=7[/tex]we get LHS = 7 and RHS = 7 which are equal.Thus, s = 7 satisfy the given equation [tex]s=4+\sqrt{s+2}[/tex].