The minimum value of the expression 3^x+3^ 1-x , x R, is - Vidyadip

MCQ

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

A
$0$
B
$\frac{1}{3}$
C
3
✓
$2 \sqrt{3}$

✓

Answer

Correct option: D.

$2 \sqrt{3}$

(D) $2 \sqrt{3}$
Explanation : We know that, A.M. $\geq$ G.M. for positive numbers.
$
\begin{array}{ll}
\text { Therefore, } & \frac{3^x+3^{1-x}}{2} \geq \sqrt{3^x \cdot 3^{1-x}} \\
\Rightarrow & \frac{3^x+3^{1-x}}{2} \geq \sqrt{3^x \cdot \frac{3}{3^x}} \\
\Rightarrow & 3^x+3^{1-x} \geq 2 \sqrt{3}
\end{array}
$

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