यदि `x=1/(2+sqrt(3)),y=1/(2-sqrt(3))` है तो `8xy(x^(2)+y^(2))` का मान क्या होगा?

Options

A. 112
B. 194
C. 290
D. 196

Answer

A

Explanation

According to the question
`implies x=1/(2+sqrt(3)),y=1/(2-sqrt(3))`
`implies x=1/(2+sqrt(3))xx(2-sqrt(3))/(2-sqrt(3))`
`y=1/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3))`
`implies x=2-sqrt(3),y=2+sqrt(3)`
`8xy(x^(2)+y^(2))`
`=8(2-sqrt(3))(2+sqrt(3))[(2-sqrt(3))^(2)+(2+sqrt(3))^(2)]`
`implies 8xx1[7-2sqrt(3)+7+2sqrt(3)]=112`