The value of `(3+2sqrt(2))^(-3)+(3-2sqrt(2))^(-3)` is

Options

A. 189
B. 180
C. 108
D. 198

Answer

D

Explanation

`(3+2sqrt(2))^(-3)+(3-2sqrt(2))^(-3)`
`=1/((3+2sqrt(2))^(3))+1/((3-2sqrt(2))^(3))`
`=1/((3)^(3)+(2sqrt(2))^(3)+(3xx3^(2)xx2sqrt(2))+(3xx3xx2sqrt(2))^(2))+`
`1/((3)^(3)-(2sqrt(2))^(3)-(3xx3^(2)xx2sqrt(2))+{3xx3xx(2sqrt(2))}^(2))`
`=1/(27+16sqrt(2)+54sqrt(2)+72)+1/(27-16sqrt(2)-54sqrt(2)+72)`
`=1/(99+70sqrt(2))+1/(99-70sqrt(2))`
`=(99-70sqrt(2)+99+70sqrt(2))/((99+70sqrt(2))(99-70sqrt(2)))`
`=198/((99)^(2)-(70sqrt(2))^(2))`
`=198/(9801-9800)=198`