(2011•浙江)设x,y为实数,若4x2+y2+xy=1,则2x+y的最大值是,这题用基本不等式怎么能算?你保证xy都正用基本不等式关键是怎么保证xy都为正数呢2X+Y 令2x=a,y=b,2X+Y=a+b4X^2+Y^2+XY=1->a^2+b^2+ab/2=1->∵[(a+b)/2
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![(2011•浙江)设x,y为实数,若4x2+y2+xy=1,则2x+y的最大值是,这题用基本不等式怎么能算?你保证xy都正用基本不等式关键是怎么保证xy都为正数呢2X+Y 令2x=a,y=b,2X+Y=a+b4X^2+Y^2+XY=1->a^2+b^2+ab/2=1->∵[(a+b)/2](/uploads/image/z/2576907-27-7.jpg?t=%282011%26%238226%3B%E6%B5%99%E6%B1%9F%29%E8%AE%BEx%2Cy%E4%B8%BA%E5%AE%9E%E6%95%B0%2C%E8%8B%A54x2%2By2%2Bxy%3D1%2C%E5%88%992x%2By%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF%2C%E8%BF%99%E9%A2%98%E7%94%A8%E5%9F%BA%E6%9C%AC%E4%B8%8D%E7%AD%89%E5%BC%8F%E6%80%8E%E4%B9%88%E8%83%BD%E7%AE%97%3F%E4%BD%A0%E4%BF%9D%E8%AF%81xy%E9%83%BD%E6%AD%A3%E7%94%A8%E5%9F%BA%E6%9C%AC%E4%B8%8D%E7%AD%89%E5%BC%8F%E5%85%B3%E9%94%AE%E6%98%AF%E6%80%8E%E4%B9%88%E4%BF%9D%E8%AF%81xy%E9%83%BD%E4%B8%BA%E6%AD%A3%E6%95%B0%E5%91%A22X%2BY+%E4%BB%A42x%3Da%2Cy%3Db%2C2X%2BY%3Da%2Bb4X%5E2%2BY%5E2%2BXY%3D1-%3Ea%5E2%2Bb%5E2%2Bab%2F2%3D1-%3E%E2%88%B5%5B%28a%2Bb%29%2F2)
(2011•浙江)设x,y为实数,若4x2+y2+xy=1,则2x+y的最大值是,这题用基本不等式怎么能算?你保证xy都正用基本不等式关键是怎么保证xy都为正数呢2X+Y 令2x=a,y=b,2X+Y=a+b4X^2+Y^2+XY=1->a^2+b^2+ab/2=1->∵[(a+b)/2
(2011•浙江)设x,y为实数,若4x2+y2+xy=1,则2x+y的最大值是,这题用基本不等式怎么能算?你保证xy都正
用基本不等式关键是怎么保证xy都为正数呢2X+Y 令2x=a,y=b,2X+Y=a+b4X^2+Y^2+XY=1->a^2+b^2+ab/2=1->∵[(a+b)/2]^2≤(a^2+b^2)/2∴->a^2+b^2+(a^2+b^2)/4-1≥a^2+b^2+ab/2-1=0所以2(a^2+b^2)≥8/5≥(a+b)^2,所以2X+Y=a+b≤√(8/5)
(2011•浙江)设x,y为实数,若4x2+y2+xy=1,则2x+y的最大值是,这题用基本不等式怎么能算?你保证xy都正用基本不等式关键是怎么保证xy都为正数呢2X+Y 令2x=a,y=b,2X+Y=a+b4X^2+Y^2+XY=1->a^2+b^2+ab/2=1->∵[(a+b)/2
楼主可知为何要保证xy都为正数