The minimum value of the expression 3^x + 3^{1 – x}, x ∈ R, is __________.

Open in App

Solution

Minimum value of 3^x + 3^{1 – x} ; x ∈ R
Since arithmetic mean ≥ geometric mean of 3^x and 3^{1 – x}
$∴ \frac{3 x + 3^{1 - x}}{2} \geq \sqrt{3^{x} 3^{1 - x}} i . e \frac{3^{x} + 3^{1 - x}}{2} \geq \sqrt{3^{x} 33^{- x}} i . e \frac{3^{x} + 3^{1 - x}}{2} = \sqrt{3} i . e 3^{x} + 3^{1 - x} \geq 2 \sqrt{3}$
i.e minimum possible value of 3^x + 3^{1 – x} is $2 \sqrt{3}$ .

Suggest Corrections

Similar questions

x \in R

3^{x} + 3^{1 - x}

| x - 1 | + | x - 2 | + | x - 3 |

x

\frac{x^{2} - 3 x + 4}{x^{2} + 3 x + 4}

\frac{x^{2}}{x^{2} + x + 1},

x \in R

x, y \in R

(x + 5)^{2} + (y - 12)^{2} - (14)^{2},

- p

Join BYJU'S Learning Program