作业帮为什么a²=4b²时,4a²b²有最大值?若a是1+2b与1-2b的等比中项,则2ab/丨a丨+2丨b丨的最大值是多少?a²＝1-4b².a²+4b²＝1[常数].∴当a²＝4b²时,4a²b²有最大值1/4|ab|
来源：学生作业帮助网 编辑：作业帮 时间：2024/09/06 12:21:53
![为什么a²=4b²时,4a²b²有最大值?若a是1+2b与1-2b的等比中项,则2ab/丨a丨+2丨b丨的最大值是多少?a²＝1-4b².a²+4b²＝1[常数].∴当a²＝4b²时,4a²b²有最大值1/4|ab|](/uploads/image/z/5227010-26-0.jpg?t=%E4%B8%BA%E4%BB%80%E4%B9%88a%26%23178%3B%3D4b%26%23178%3B%E6%97%B6%2C4a%26%23178%3Bb%26%23178%3B%E6%9C%89%E6%9C%80%E5%A4%A7%E5%80%BC%3F%E8%8B%A5a%E6%98%AF1%2B2b%E4%B8%8E1-2b%E7%9A%84%E7%AD%89%E6%AF%94%E4%B8%AD%E9%A1%B9%2C%E5%88%992ab%2F%E4%B8%A8a%E4%B8%A8%2B2%E4%B8%A8b%E4%B8%A8%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91%3Fa%26%23178%3B%EF%BC%9D1-4b%26%23178%3B.a%26%23178%3B%2B4b%26%23178%3B%EF%BC%9D1%5B%E5%B8%B8%E6%95%B0%5D.%E2%88%B4%E5%BD%93a%26%23178%3B%EF%BC%9D4b%26%23178%3B%E6%97%B6%2C4a%26%23178%3Bb%26%23178%3B%E6%9C%89%E6%9C%80%E5%A4%A7%E5%80%BC1%2F4%7Cab%7C)
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为什么a²=4b²时,4a²b²有最大值?若a是1+2b与1-2b的等比中项,则2ab/丨a丨+2丨b丨的最大值是多少?a²＝1-4b².a²+4b²＝1[常数].∴当a²＝4b²时,4a²b²有最大值1/4|ab|
为什么a²=4b²时,4a²b²有最大值?
若a是1+2b与1-2b的等比中项,则2ab/丨a丨+2丨b丨的最大值是多少?
a²＝1-4b².a²+4b²＝1[常数].∴当a²＝4b²时,4a²b²有最大值1/4
|ab|最大值1/4,令2ab/丨a丨+2丨b丨＝k
则 k²＝4a²b²/（a²+4|ab|+4b²）＝4a²b²/（4|ab|+1）[硬除]
＝|ab|-1/4+1/（4|ab|+1）[配方]
＝（1/4）[√（|ab|+1）-1/√（4|ab|+1）]²
k＝±[√（|ab|+1）-1/√（4|ab|+1）]/2.当|ab|＝1/4（最大）时.
k有最大值√2/4 [最大-最小＝最大]
为什么a²=4b²时,4a²b²有最大值?若a是1+2b与1-2b的等比中项,则2ab/丨a丨+2丨b丨的最大值是多少?a²＝1-4b².a²+4b²＝1[常数].∴当a²＝4b²时,4a²b²有最大值1/4|ab|
有基本不等式 a+b≥2√ab (a,b都是正数) 等号成立的条件为a=b
当a+b=m时(m为常数),m=a+b≥2√ab 则当a=b时,ab取得最大值m^2/4
在本题中 1=a²+4b²≥2√(a²*4b²)
所以当a²＝4b²时,4a²b²有最大值1/4