急救!若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.答案要容易懂,
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![急救!若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.答案要容易懂,](/uploads/image/z/5444361-9-1.jpg?t=%E6%80%A5%E6%95%91%21%E8%8B%A5a%3E0%2Cb%3E0%2C%E4%B8%94a%2Bb%3Dc.%E6%B1%82%E8%AF%81%3A%281%29%E5%BD%93r%EF%BC%9E1%E6%97%B6a%EF%BC%BEr%2Bb%EF%BC%BEr%EF%BC%9Cc%EF%BC%BEr%3B%282%29%E5%BD%93r%EF%BC%9C1%E6%97%B6a%EF%BC%BEr%2Bb%EF%BC%BEr%EF%BC%9Ec%EF%BC%BEr.%E8%8B%A5a%3E0%2Cb%3E0%2C%E4%B8%94a%2Bb%3Dc.%E6%B1%82%E8%AF%81%3A%281%29%E5%BD%93r%EF%BC%9E1%E6%97%B6a%EF%BC%BEr%2Bb%EF%BC%BEr%EF%BC%9Cc%EF%BC%BEr%3B%282%29%E5%BD%93r%EF%BC%9C1%E6%97%B6a%EF%BC%BEr%2Bb%EF%BC%BEr%EF%BC%9Ec%EF%BC%BEr.%E7%AD%94%E6%A1%88%E8%A6%81%E5%AE%B9%E6%98%93%E6%87%82%2C)
急救!若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.答案要容易懂,
急救!若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.
若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.
答案要容易懂,
急救!若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.若a>0,b>0,且a+b=c.求证:(1)当r>1时a^r+b^r<c^r;(2)当r<1时a^r+b^r>c^r.答案要容易懂,
a+b=c
a/c+b/c=1其中a/c,b/c均小于1大于零
构造函数Y=(a/c)^X+(b/c)^X
当X大于1时,Y
^ 是乘号 × ?
若果是,那么就先把 a=b+c 换算为b=c-a 同理换算其他值 ,很简单的,上面那个大哥把过程写出来的,就是代算很麻烦而已,加油!
作差:S=a/(1+a)+b/(1+b)-c/(1+c)
=[a(1+b)(1+c)+b(1+a)(1+c)-c(1+a)(1+b)]/[(1+a)(1+b)(1+c)]
=(a+ac+ab+abc+b+bc+ab+abc-c-ac-bc-abc)/[(1+a)(1+b)(1+c)]
=(a+2ab+abc)/[(1+a)(1+b)(1+c)]>0
∴a/(1+a)+b/(1+b)>c/(1+c)
抱歉 刚少了个a Y