If `x in R ,` the numbers `2^(1+x)+2^(1-x), b//2,36^x+36^(-x)` form an A.P., then `b` may lie in the interval `[12 ,oo)` b. `[6,oo)` c. `(-oo,6]` d. `[6, 12]`

Options

A. `[12, oo)`
B. `[6, oo)`
C. `(-oo, 6]`
D. `[6, 12]`

Answer

B

Explanation

If `x in R`, the numbers ………….
`b = (2^(t+x)+2^(t-x))+(36^(x)+36^(-x))`
` = 2underset(ge2)underbrace((2^(x)+2^(-x))) + underset(ge2)underbrace((6^(2x)+6^(-2x)))`
`implies b ge 2(2)+2 = 6`
`i.e. b in [6, oo)`