不等式的证明方法1.a³+b³=2,求证a+b≤2(用反证法解)2.已知x²+y²=4,求2x+3y的取值范围(用换元法解)3.若a,b,c,d∈R+,求证:1<(a/a+b+d)+(b/b+c+a)+(c/c+d+b)+(d/d+a+c)<2(用
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 03:32:32
![不等式的证明方法1.a³+b³=2,求证a+b≤2(用反证法解)2.已知x²+y²=4,求2x+3y的取值范围(用换元法解)3.若a,b,c,d∈R+,求证:1<(a/a+b+d)+(b/b+c+a)+(c/c+d+b)+(d/d+a+c)<2(用](/uploads/image/z/9641479-31-9.jpg?t=%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%9A%84%E8%AF%81%E6%98%8E%E6%96%B9%E6%B3%951.a%26sup3%3B%2Bb%26sup3%3B%3D2%2C%E6%B1%82%E8%AF%81a%2Bb%E2%89%A42%EF%BC%88%E7%94%A8%E5%8F%8D%E8%AF%81%E6%B3%95%E8%A7%A3%EF%BC%892.%E5%B7%B2%E7%9F%A5x%26sup2%3B%2By%26sup2%3B%3D4%2C%E6%B1%822x%2B3y%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%28%E7%94%A8%E6%8D%A2%E5%85%83%E6%B3%95%E8%A7%A3%293.%E8%8B%A5a%2Cb%2Cc%2Cd%E2%88%88R%EF%BC%8B%2C%E6%B1%82%E8%AF%81%EF%BC%9A1%EF%BC%9C%EF%BC%88a%EF%BC%8Fa%2Bb%2Bd%EF%BC%89%2B%EF%BC%88b%EF%BC%8Fb%2Bc%2Ba%EF%BC%89%2B%EF%BC%88c%EF%BC%8Fc%2Bd%2Bb%EF%BC%89%2B%EF%BC%88d%EF%BC%8Fd%2Ba%2Bc%EF%BC%89%EF%BC%9C2%EF%BC%88%E7%94%A8)
不等式的证明方法1.a³+b³=2,求证a+b≤2(用反证法解)2.已知x²+y²=4,求2x+3y的取值范围(用换元法解)3.若a,b,c,d∈R+,求证:1<(a/a+b+d)+(b/b+c+a)+(c/c+d+b)+(d/d+a+c)<2(用
不等式的证明方法
1.a³+b³=2,求证a+b≤2(用反证法解)
2.已知x²+y²=4,求2x+3y的取值范围(用换元法解)
3.若a,b,c,d∈R+,求证:1<(a/a+b+d)+(b/b+c+a)+(c/c+d+b)+(d/d+a+c)<2(用放缩法解)
4.求证:1/2≤(x²+x+1)/(x²+1)≤3/2(用判别式法解)
(这是我暑假预习作业上的,由于还没学,麻烦帮忙把各种方法说详细点,
不等式的证明方法1.a³+b³=2,求证a+b≤2(用反证法解)2.已知x²+y²=4,求2x+3y的取值范围(用换元法解)3.若a,b,c,d∈R+,求证:1<(a/a+b+d)+(b/b+c+a)+(c/c+d+b)+(d/d+a+c)<2(用
假设a+b>2,则
a³+b³=(a+b)(a^2+b^2-ab)>
(a+b)(a^2+b^2-(a^2+b^2)/2)>
(a+b)(a^2+b^2)/2)>2
与原题矛盾,假设不成立.
a+b≤2
令x=2cosx,y=2sinx
则:2x+3y=2*(2cosx+3siny)=2根号(2^2+3^2)sin(x+θ)
则取值范围为[-2根号13,2根号13]
(a/a+b+d)>a/(a+b+c+d)
(b/b+c+a)>b/(a+b+c+d)
(c/c+d+b)>c/(a+b+c+d)
(d/d+a+c)>d/(a+b+c+d)
两边相加
则(a/a+b+d)+(b/b+c+a)+(c/c+d+b)+(d/d+a+c)>1
(a/a+b+d)