Find the minimum value of the expression, $P = 2^{x + 1} + \frac{1}{[4^{(\frac{x}{2} + \frac{3}{2})}]}$ , given that x is real

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Solution

The correct option is B 1
The expression can be rewritten as

$2^{x + 1} + 2^{- 2 (\frac{x}{2} + \frac{3}{2})}$

$= 2^{x + 1} + 2^{- x - 3}$

$= 2^{x + 1} + 2^{- 2} 2^{- x - 1}$

Using the concept of AM $\geq$ GM

The minimum value of the given expression = 1.

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