1.

Let alpha=sqrt(19-8sqrt3)+sqrt(7+4sqrt3)and beta=sqrt(83-18sqrt2)-sqrt(6-4sqrt2),then log_(2)((alpha)/(beta)) lies in the interval

Answer»

`(-2,-1)`
`((-1)/(2),0)`
`(0,1)`
`(-1,(-1)/(2))`

Solution :`ALPHA=(4-sqrt3)+(2+sqrt3)=6AND beta=(9-sqrt2)-(2-sqrt2)=7.`
`thereforelog_(2)((alpha)/(beta))=log_(2)((6)/(7))`
`As,(1)/(sqrt2)lt6/7lt1implies(-1)/(2)ltlog_(2)((6)/(7))LT0`


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