If `(4+3sqrt(3))/(sqrt(7+4sqrt(3)))=A+sqrt(B)` then B-A is

Options

A. `-13`
B. `2sqrt(13)`
C. 13
D. `3sqrt(3)-7`

Answer

C

Explanation

`(4+3 sqrt(3))/(sqrt(7+4 sqrt(3)))=A+ sqrt(B)`
`rAr (4+3 sqrt(3))/(sqrt((2)^(2)+(sqrt(3))^(2)+2xx2xx sqrt(3)))=A+ sqrt(B)`
`rArr A+ sqrt(B)=(4+3 sqrt(3))/(2+sqrt(3))xx(2- sqrt(3))/(2- sqrt(3))`
`rArr A+ sqrt(B)=((8-4 sqrt(3)+6 sqrt(3)-9))/(4-3)`
`rArr A+ sqrt(B)=-1+2 sqrt(3)=-1+ sqrt(12)`
`rArr A=-1, B=12`
`rArr :. B-A=12-(-1)=12+1=13`