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The sum of the roots of the equation 2^(...

The sum of the roots of the equation `2^(33 x-2)+2^(11 x+2)=2^(22 x+1)+1` is

A

`1/11`

B

`2/11`

C

`3/11`

D

`4/11`

Text Solution

Verified by Experts

Let `2^(11x)=t`, given equation reduces to
`(t^(3))/4+4t=2t^(2)+1`
`impliest^(3)-8t^(2)+16t-4=0impliest_(1).t_(2).t_(3)=4`
`implies2^(11x_(1)).2^(11x_(3))=4implies2^(11(x_(1)+x_(2)+x_(3)))=2^(2)`
`implies11(x_(1)+x_(2)+x_(3))=2`
`:.x_(1)+x_(2)+x_(3)=2/11`
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