Find the minimum value of the expression, P = 2^x+1 + 1/ [4^{(x/2 + 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 (x/2 +3/2)}
= 2x+1 + 2 ^-x-3
Using the concept of AM ≥ GM
Therefore, the min value occurs when both the numbers are same. In that case 2^(x+1)= 2^-(x+3). X = -2. Thus the number = ½.so ½ +1/2 = 1.

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