Fill in the blanks If `x<0,y<0,x+y+(x//y)=(1//2)a n d(x+y)(x//y)=-(1//2),t h e nx=______________`
` and y=__________dot`

Answer

`-1 and 2`

Explanation

Since, `x gt 0, y lt 0`
`and x+y+(x)/(y) =(1)/(2)`
`and (x+y) *(x)/(y)= -(1)/(2) rArr -(y)/(2x)+(x)/(y)+(1)/(2)`
Let `(x)/(y) =t`
`rArr -(1)/(2t)+t=(1)/(2)`
`rArr 2t^(2)-1=t rArr 2t^(2)-t-1=0`
`therefore t= -(1)/(2) ["but "x gt 0 and y lt 0 therefore (x)/(y) lt 0 " neglecting "1]`
`rArr (x)/(y) = -(1)/(2) rArr y=-2x rArr x+y+(x)/(y) =(1)/(2)`
`rArr x-2x-(1)/(2) =(1)/(2) rArr x= -1 and y=2`