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To the equation 2^(2pi//cos^(-1)x) - (a ...

To the equation `2^(2pi//cos^(-1)x) - (a + (1)/(2)) 2^(pi/cos^(-1)x) -a^(2) = 0` has only one real root, then

A

`(-3, 1)`

B

`(-oo,-3]`

C

`[1,oo)`

D

`[-3,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Let `2^((pi)/(cos^(-1)x))=timpliestge2`
`:.` equation becomes `t^(2)-(a+1/2)t-a^(2)=0`
has one root 2 or greater than 2 & other root less than `2impliesf(2)le0`
`implies4-(a+1/2):2-a^(2)le0`
`a^(2)+2a-3ge0`
`(a+3)(a-1)ge0`
`impliesale-3` or `age1`
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