Question

Find the number of all the integral solutions of the inequality $\frac{(x^2+2)\left(\sqrt{x^2-16}\right)}{(x^4+2)(x^2-9)}\le 0$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$\frac{(x^2+2)\sqrt{x^2-16}}{(x^4+2)(x^2-9)}\le 0x^2+2>0,\sqrt{x^2-16}>0,x^4+2>0\frac{1}{x^2-9}\le 0\frac{1}{(x-3)(x+3)}\le 0x\in \{-2,-1,0,1,2\}{x}^2-16>0x^2>16$

$x^2-9<0$ and $x^2-16>0$ cant be possible at a time.

$\therefore$ Given equation is valid only at $x^2-16=0$

$\therefore x=\pm 4$