Question

Find the number of integral roots the equation $\sqrt{9-{(n+2)}^2}$

Answer 1

$\sqrt{9-(n+2{)}^2}\ge 0$

$\Rightarrow$$9-(n+2{)}^2\ge 0$

$\Rightarrow$$3^2-(n+2{)}^2\ge 0$

$\Rightarrow$$(n+2{)}^2-3^2\le 0$

$\Rightarrow$$(n+2-3)(n+2+3)\le 0$

$\Rightarrow$$(n-1)(n+5)\le 0$

$\Rightarrow$$n\in [-5,+1]$

$\therefore$ $n$ takes $-5,-4,-3,-2,-1,0,1$ values

$\therefore$ numbers of integral values $=7$.