Question

The set of all $x$ satisfying, $4^{x^2+2}-9\left(2^{x^2+2}\right)+8=0$, consists of

• A. Infinitely many points
• B. Four integer points
• C. Two integer points
• D. None of these

Answer 1

The correct option is C Two integer points

$4^{x^2+2}-9\left(2^{x^2+2}\right)+8=0$

Let $2^{x^2+2}=p$

So $p^2-9p+8=0$

$\Rightarrow (p-8)(p-1)=0$

So $P=1$ or $P=8$

$2^{x^2+2}=1$ or $2^{x^2+2}=8$

$\Rightarrow 2^{x^2+2}=2^0$ or $2^{x^2+2}=2^3$

comparing the powers

$x^2+2=0$ $x^2=1$

$x=\pm \sqrt{-2}$ $x=\pm 1$