Question

$x{y}^2+x-y^2-1=0$
If the equation above is true for all real values of y. what must the values of x be?

Answer 1

$x{y}^2+x-y^2-1=0$

$\Rightarrow x(y^2+1)-1(y^2+1)=0$

$\Rightarrow (x-1)(y^2+1)=0$

$\therefore x=1,y=\pm \sqrt{-1}=\pm i$

Hence $x=1$