`(3+2sqrt(2))^(-3)+(3-2sqrt(2))^(-3)` का मान ज्ञात करें।

Options

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

Answer

D

Explanation

`(3+2sqrt(2))^(-3)+(3-2sqrt(2))^(-3)`
`implies(1/(3+2sqrt(2)))^(3)+(1/(3-2sqrt(2)))^(3)`
`implies (1/((3-2sqrt(2)))xx(3+2sqrt(2))/(3+2sqrt(2)))^(3)+(1/((3+2sqrt(2)))xx(3-2sqrt(2))/(3-2sqrt(2)))^(3)`
`implies ((3-2sqrt(2))/(9-8))^(3)+((3+2sqrt(2))/(9-8))^(3)`
`implies(3-2sqrt(2))^(3)+(3+2sqrt(2))^(3)`
`a=3-2sqrt(2)`
`b=3+2sqrt(2)`
`a^(3)+b^(3)implies(a+b)(a^(2)+b^(2)-ab)`
`implies(3-2sqrt(2)+3+2sqrt(2))(17+17-1)`
`implies (6)(33)`
`implies 198`