Find all real numbers x and y such that 2x^2 + y^2 - 2xy + 12y + 72 <= 0.
x^2-2xy+y^2+x^2+12y+72 <= 0
(x-y)^2+x^2+12y+72 <= 0
(x-y)^2 has to be greater than or equal to 0.
x^2 has to be greater than or equal to 0.
So 12y+72 has to be less than or equal to 0.
Based on this, can you find it?
You are very welcome!