若正数a,b满足ab=a+b+3,则ab的取值范围是? 为什么我会算出(0,1]和[9,+∞)两个范围ab=a+b+3 a+b=ab-3 (a+b)^2≥4ab(a+b)^2=(ab-3)^2=(ab)^2-6ab+9≥4ab (ab)^2-10ab+9≥0(ab-9)(ab-1)≥0得(0,1]和[9,+∞)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/07 03:06:54
![若正数a,b满足ab=a+b+3,则ab的取值范围是? 为什么我会算出(0,1]和[9,+∞)两个范围ab=a+b+3 a+b=ab-3 (a+b)^2≥4ab(a+b)^2=(ab-3)^2=(ab)^2-6ab+9≥4ab (ab)^2-10ab+9≥0(ab-9)(ab-1)≥0得(0,1]和[9,+∞)](/uploads/image/z/13865941-37-1.jpg?t=%E8%8B%A5%E6%AD%A3%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3ab%3Da%2Bb%2B3%2C%E5%88%99ab%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%3F+%E4%B8%BA%E4%BB%80%E4%B9%88%E6%88%91%E4%BC%9A%E7%AE%97%E5%87%BA%EF%BC%880%2C1%5D%E5%92%8C%5B9%2C%2B%E2%88%9E%EF%BC%89%E4%B8%A4%E4%B8%AA%E8%8C%83%E5%9B%B4ab%3Da%2Bb%2B3++a%2Bb%3Dab-3+++++%EF%BC%88a%2Bb%EF%BC%89%5E2%E2%89%A54ab%EF%BC%88a%2Bb%EF%BC%89%5E2%3D%EF%BC%88ab-3%EF%BC%89%5E2%3D%28ab%29%5E2-6ab%2B9%E2%89%A54ab++%28ab%29%5E2-10ab%2B9%E2%89%A50%28ab-9%29%28ab-1%29%E2%89%A50%E5%BE%97%EF%BC%880%2C1%5D%E5%92%8C%5B9%2C%2B%E2%88%9E%EF%BC%89)
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