For real numbers x and y, if `x^2+xy-y^2+2x -y+1=0`, then (a) y can not be between 0 and `8/5` (b) y can not be between `-8/5 and 8/5` (c) y cannnot be between `-8/5 and 0`(d) y cannot be between `-16/5 and 0`

Explanation

`x^2+x(y+2)-y^2-y+1=0`

`D>=0`

`(y+2)^2-4(-y^2-y+1)>=0`

`y^2+4+4y+4y^2+4y-4>=0`

`5y^2+8y>=0`

`y(5y+8)>=0`

`(-8/5,0)`

Option C is correct.