यदि `x=3+2sqrt(2)` और `xy=1` है तो `(x^(2)+3xy+y^(2))/(x^(2)-3xy+y^(2))` का मान ज्ञात करें।

Options

A. `30/31`
B. `70/31`
C. `35/31`
D. `37/31`

Answer

D

Explanation

`x=3+2sqrt(2),xy=1,y^(2)=1/(x^(2))`
`y=1/x=1/(3+2sqrt(2))=3-2sqrt(2)`
`:. x+1/x=3+2sqrt(2)+3-2sqrt(2)=6`
`:. x^(2)+1/(x^(2))=36-2=34`
`= (x^(2)+3xy+y^(2))/(x^(2)-3xy+y^(2))=(x^(2)+1/(x^(2))+3)/(x^(2)+1/(x^(2))-3)`
`=(34+3)/(34-3)=37/31`