已知实数x,y满足x2+2xy+3y2-8y+6=0,求x,y的取值范围
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![已知实数x,y满足x2+2xy+3y2-8y+6=0,求x,y的取值范围](/uploads/image/z/6891109-61-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3x2%2B2xy%2B3y2-8y%2B6%3D0%2C%E6%B1%82x%2Cy%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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