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Number of solution of $2\cos^2(\large\frac{x}{2})=$$(0.2)^x+(0.2)^{-x}$ are

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;2&(D)\;\text{infinite}\end{array} $

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Maximum value of $\cos^2(\large\frac{x}{2})$$=1$
$\Rightarrow 2\cos^2(\large\frac{x}{2}) $$\leq 2$
Minimum value of $(0.2)^x+(0.2)^{-x}$ is 2
$\Rightarrow (0.2)^x+(0.2)^{-x}\geq 2$
Thus LHS=RHS=2 when $x=0$.
Thus only one solution is possible.
Hence (B) is the correct answer.
answered Apr 16, 2014 by sreemathi.v

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