1.

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

Answer» Correct Answer - B
`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)`


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