यदि `x=1+sqrt(2)` और `y=1-sqrt(2)` तो `x^(-2)+y^(-2)` का मान क्या होगा।

Options

A. 8
B. 4
C. 6
D. 2

Answer

C

Explanation

`(1)/(x)=(1)/(1+sqrt(2))xx(1-sqrt(2))/(1-sqrt(2))implies(1-sqrt(2))/(-1)impliessqrt(2)-1`
`(1)/(y)=(1)/(1-sqrt(2))xx(1+sqrt(2))/(1+sqrt(2))implies(1+sqrt(2))/(1-2)implies-1-sqrt(2)`
`:.x^(-2)+y^(-2)=(1)/(x^(2))+(1)/(y^(2))`
`:.x^(-2)+y^(-2)=(sqrt(2)-1)^(2)+(-1-sqrt(2))^(2)`
`=2+1-2sqrt(2)+1+2+2sqrt(2)=6`