Question

The number of integral values of x satisfying $\sqrt{-x^2+10x-16}<x-2$ is

• A. 3
• B. 2
• C. 4
• D. 5

Answer 1

The correct option is A 3

$\mathrm{The}\mathrm{quantity}\mathrm{in}\mathrm{square}\mathrm{root}\mathrm{must}\mathrm{be}\mathrm{non}-\mathrm{negative}-x^2+10x-16\ge 0\mathrm{or},x^2-10x+16\le 0\mathrm{or},(x-2)(x-8)\le 0$
$\Rightarrow 2\le x\le 8......\left[1\right]\mathrm{Also}\mathrm{on}\mathrm{squaring}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}-x^2+10x-16<x^2-4x+4\Rightarrow 2x^2-14x+20>0\Rightarrow x^2-7x+10>0\Rightarrow x>5\mathrm{or}x<2.......\left[2\right]\mathrm{From}\left[1\right]\mathrm{and}\left[2\right]\mathrm{we}\mathrm{get},5<x\le 8\Rightarrow x=6,7,8$