4x^2-4x+y^2+10y+27
=(2x)²-4x+1²+y²+10y+5²+1
=(2x-1)²+(y+5)²+1
因为(2x-1)²,(y+5)²无论xy取何值都大于等于0
所以(2x-1)²+(y+5)²+1大于等于1
所以无论x,y为何值,4x^2-4x+y^2+10y+27的值恒为正