Question

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

• A. $0$
• B. $\frac{1}{3}$
• C. $3$
• D. $2\sqrt{3}$

Answer 1

Answer: (D)

We know that $A.M.\ge G.M$. for positive numbers.
Therefore, $\frac{3^x+3^{1-x}}{2}\ge \sqrt{3^x\cdot 3^{1-x}}$
$\Rightarrow 3^x+3^{1-x}\ge 2\sqrt{3}$