Question

The number of solution of the equation $2\cos \left(\frac{x}{4}\right)=4^x+4^{-x}$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

$\text{ R.H.S }=4^x+\frac{1}{4^x}\ge 2$
$\text{ L.H.S }=2\cos \left(\frac{x}{4}\right)\in [-2,2]$
$\therefore$ Equation has solution when $4^x+\frac{1}{4^x}=2\Rightarrow x=0$
$x=0$ is only possible solution.