Question

x la 2+ 5y la 2 -2xy -12y + 9= 0 x+y=?

Answer 1

$x^2+5y^2-2xy-12y+9=0\\x^2-2xy+y^2+4y^2-12y+9=0\\(x-y)^2+4y^2-12y+8+1=0\\(x-y)^2+(2y-3)^2=0 \implies (x-y)^2=0, (2y-3)^2=0\\x-y=0 \implies x=y\\2y-3=0 \implies y=\frac{3}{2} \\x=y=\frac{3}{2} \\\boxed{x+y=\frac{3}{2} +\frac{3}{2} =3}$