Question

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

Options

• 0

• `1/3`

• 3

• `2sqrt(3)`

Answer 1

The minimum value of the expression 3^x + 3^1–x, x ∈ R, is `2sqrt(3)`.

Explanation:

We know A.M. ≥ G.M. for positive numbers.

Therefore, `(3^x 6 3(1 - x))/2 ≥ sqrt(3^x * 3^(1 - x))`

⇒ `(3^x + 3^(l - x))/2 ≥ sqrt(3^x * 3/3^x)`

⇒ `3^x + 3^(1 - x) ≥ 2sqrt(3)`