已知实数x,y满足x2+2xy+3y2-8y+6=0,求x,y的取值范围

已知实数x,y满足x2+2xy+3y2-8y+6=0,求x,y的取值范围
已知实数x,y满足x2+2xy+3y2-8y+6=0,求x,y的取值范围

已知实数x,y满足x2+2xy+3y2-8y+6=0,求x,y的取值范围
x2+2xy+3y2-8y+6=0
而,x^2+2xy+3y^2-8y+6=(x+y)^2+2y^2-8y+6
=(x+y)^2+2(y-2)^2-2=0
（x+y)^2+2(y-2)^2=2
所以,|y-2|

原式等于x²+2xy+y²+2y²-8y+6=0
（x+y）²+（ y-3）（2y-2）=0
（x+y）²大于等于0
（ y-3）（2y-2）小于等于0
解出y，根据y写x