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  4. The number of solution of the equation 2 cos ((x/4))=4x+4-x is

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

Complex Numbers and Quadratic Equations

Solution:

$ \text { R.H.S }=4^x+\frac{1}{4^x} \geq 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.