Question

If $x\in R$, find the minimum value of the expression $3^x+3^{1-x}$.

• A. $3\sqrt{2}$
• B. $2\sqrt{3}$
• C. $3\sqrt{3}$
• D. none of these

Answer 1

The correct option is B $2\sqrt{3}$

We know,

$AM>GM$

Therefore,

$\frac{3^x+3^{1-x}}{2}\ge \sqrt{3^x\times 3^{1-x}}$ for all $x\in R$.

$\frac{3^x+3^{1-x}}{2}\ge \sqrt{3}$ for all $x\in R$.

$3^x+3^{1-x}\ge 2\sqrt{3}$ for all $x\in R$

Hence, the required value is $2\sqrt{3}$.