如何证明x²+xy+y²≥3x+3y-3? (其实就是证明xy+1≥x+y,可怎么证明呢?)(其实就是证明xy+1≥x+y,可怎么证明呢?)这是错的。条件x,y∈R
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 03:44:06
![如何证明x²+xy+y²≥3x+3y-3? (其实就是证明xy+1≥x+y,可怎么证明呢?)(其实就是证明xy+1≥x+y,可怎么证明呢?)这是错的。条件x,y∈R](/uploads/image/z/812938-58-8.jpg?t=%E5%A6%82%E4%BD%95%E8%AF%81%E6%98%8Ex%26%23178%3B%2Bxy%2By%26%23178%3B%E2%89%A53x%2B3y-3%3F+%EF%BC%88%E5%85%B6%E5%AE%9E%E5%B0%B1%E6%98%AF%E8%AF%81%E6%98%8Exy%2B1%E2%89%A5x%2By%2C%E5%8F%AF%E6%80%8E%E4%B9%88%E8%AF%81%E6%98%8E%E5%91%A2%3F%EF%BC%89%EF%BC%88%E5%85%B6%E5%AE%9E%E5%B0%B1%E6%98%AF%E8%AF%81%E6%98%8Exy%2B1%E2%89%A5x%2By%EF%BC%8C%E5%8F%AF%E6%80%8E%E4%B9%88%E8%AF%81%E6%98%8E%E5%91%A2%EF%BC%9F%EF%BC%89%E8%BF%99%E6%98%AF%E9%94%99%E7%9A%84%E3%80%82%E6%9D%A1%E4%BB%B6x%2Cy%E2%88%88R)
如何证明x²+xy+y²≥3x+3y-3? (其实就是证明xy+1≥x+y,可怎么证明呢?)(其实就是证明xy+1≥x+y,可怎么证明呢?)这是错的。条件x,y∈R
如何证明x²+xy+y²≥3x+3y-3? (其实就是证明xy+1≥x+y,可怎么证明呢?)
(其实就是证明xy+1≥x+y,可怎么证明呢?)这是错的。条件x,y∈R
如何证明x²+xy+y²≥3x+3y-3? (其实就是证明xy+1≥x+y,可怎么证明呢?)(其实就是证明xy+1≥x+y,可怎么证明呢?)这是错的。条件x,y∈R
证明:(x²+xy+y²)-(3x+3y-3)=x²+x(y-3)+y²-3y+3
=[x+(y-3)/2]²+(y²-3y+3)-(y-3)²/4
=[x+(y-3)/2]²+3(y-1)²/4≥0
则x²+xy+y²≥3x+3y-3
条件不全,无法解出
楼上两位:这道题应该是解得出的,有图有真相:
令x=1/y
带入
得:2≥1/y+y ①
通分
得:y≥1 ②
至于这个结果,应该有其他条件吧?
或者①之后,
根据基本不等式
2≤1/y+y
出相反的结果