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

Options

A. `sqrt(3)`
B. `3sqrt(3)`
C. `16sqrt(3)`
D. `2sqrt(3)`

Answer

B

Explanation

`x=sqrt(3)-1/(sqrt(3))` & `y=sqrt(3)+1/(sqrt(3))`
`implies (x^(2))/y+(y^(2))/x=(x^(3)+y^(3))/(xy)`
`=((x+y)(x^(2)-xy+y^(2)))/(xy)`
`:. x+y=sqrt(3)-1/(sqrt(3))+sqrt(3)+1/(sqrt(3))=2sqrt(3)`
`:. Xy=(sqrt(3)-1/(sqrt(3)))(sqrt(3)+1/(sqrt(3)))`
`=3-1/3=8/3`
`implies ((x+y)(x^(2)+y^(2)+2xy-2xy-xy))/(xy)`
`implies ((x+y)((x+y)^(2)-3xy))/(xy)`
`implies (2sqrt(3)((2sqrt(3))^(2)-3xx8/3))/(8/3)`
`implies (2sqrt(3)(12-8))/(8/3)implies (2xx3sqrt(3)(4))/8=3sqrt(3)`