Question

If `x in R ,` find the minimum value of the expression `3^x+3^(1-x)dot`

Answer 1

We known that `AM gt GM`.
`:.` for all `x in R`, we have
`(3^(x)+3^((1-x)))/2 gt sqrt(3^(x)xx3^((1-x)))`
`rArr (3^(x)+3^((1-x)))/2 gt sqrt(3)`
`rArr {3^(x)+3^((1-x))} gt 2sqrt(3)`.
Hence, the minimum value of `3^(x)+3^((1-x))` is `2sqrt(3)` for any `x in R`.