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If y=3^(x-1)+3^(-x-1) , then the least v...

If `y=3^(x-1)+3^(-x-1)` , then the least value of `y` is

A

2

B

6

C

`2//3`

D

`3//2`

Text Solution

Verified by Experts

The correct Answer is:
C
`y = (3^(x))/(3) + (1)/(3^(x) 3)`
Now,
`A.M ge G.M`
`implies ((3^(x))/(3) + (1)/(3^(3^(x) 3)))^(2) ge sqrt((3^(x))/(3) (1)/(3^(x) 3))`
Or `3^(x - 1) + 3^(-x - 1) ge (2)/(3)`
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