First slide

Means - A.M/G.M/H.M

Question

$The minimum value of the expression 3^{x} + 3^{1 - x}, x \in R is:$

Moderate

A

0
B

$\frac{1}{3}$
C

3
D

$2 \sqrt{3}$

Solution

$A. M \geq G.M$
$\begin{array}{l} \frac{3^{x} + 3^{1 - x}}{2} \geq \sqrt{3^{x} \cdot 3^{1 - x}} \\ 3^{x} + 3^{1 - x} \geq 2 \sqrt{3} \end{array}$

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