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Answer» Correct Answer - `-1 and 2` 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` |
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