柯西不等式证明:若abc=1,1/(√a)+1/(√b)+1/(√c)xiejings_88:(√abc)=1/(√a)+1/(√b)+1/(√c)这是什么意思是否写错与下文不符(a+b+c)(b+c+a)>=(√bc+√ac+√ab)^2即:(a+b+c)>=(√bc+√ac+√ab) 当a/b=b/c=c/a 即a=b=c时取
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![柯西不等式证明:若abc=1,1/(√a)+1/(√b)+1/(√c)xiejings_88:(√abc)=1/(√a)+1/(√b)+1/(√c)这是什么意思是否写错与下文不符(a+b+c)(b+c+a)>=(√bc+√ac+√ab)^2即:(a+b+c)>=(√bc+√ac+√ab) 当a/b=b/c=c/a 即a=b=c时取](/uploads/image/z/1097333-53-3.jpg?t=%E6%9F%AF%E8%A5%BF%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%AF%81%E6%98%8E%3A%E8%8B%A5abc%3D1%2C1%2F%28%E2%88%9Aa%29%2B1%2F%28%E2%88%9Ab%29%2B1%2F%28%E2%88%9Ac%29xiejings_88%3A%28%E2%88%9Aabc%29%3D1%2F%28%E2%88%9Aa%29%2B1%2F%28%E2%88%9Ab%29%2B1%2F%28%E2%88%9Ac%29%E8%BF%99%E6%98%AF%E4%BB%80%E4%B9%88%E6%84%8F%E6%80%9D%E6%98%AF%E5%90%A6%E5%86%99%E9%94%99%E4%B8%8E%E4%B8%8B%E6%96%87%E4%B8%8D%E7%AC%A6%28a%2Bb%2Bc%29%28b%2Bc%2Ba%29%3E%3D%28%E2%88%9Abc%2B%E2%88%9Aac%2B%E2%88%9Aab%29%5E2%E5%8D%B3%EF%BC%9A%28a%2Bb%2Bc%29%3E%3D%28%E2%88%9Abc%2B%E2%88%9Aac%2B%E2%88%9Aab%29+%E5%BD%93a%2Fb%3Db%2Fc%3Dc%2Fa+%E5%8D%B3a%3Db%3Dc%E6%97%B6%E5%8F%96)
柯西不等式证明:若abc=1,1/(√a)+1/(√b)+1/(√c)xiejings_88:(√abc)=1/(√a)+1/(√b)+1/(√c)这是什么意思是否写错与下文不符(a+b+c)(b+c+a)>=(√bc+√ac+√ab)^2即:(a+b+c)>=(√bc+√ac+√ab) 当a/b=b/c=c/a 即a=b=c时取
柯西不等式证明:若abc=1,1/(√a)+1/(√b)+1/(√c)
xiejings_88:
(√abc)=1/(√a)+1/(√b)+1/(√c)这是什么意思
是否写错
与下文不符
(a+b+c)(b+c+a)>=(√bc+√ac+√ab)^2
即:(a+b+c)>=(√bc+√ac+√ab) 当a/b=b/c=c/a 即a=b=c时取等号。
证得好
柯西不等式证明:若abc=1,1/(√a)+1/(√b)+1/(√c)xiejings_88:(√abc)=1/(√a)+1/(√b)+1/(√c)这是什么意思是否写错与下文不符(a+b+c)(b+c+a)>=(√bc+√ac+√ab)^2即:(a+b+c)>=(√bc+√ac+√ab) 当a/b=b/c=c/a 即a=b=c时取
abc=1 (√abc)=1 (√abc) =
1/(√a)+1/(√b)+1/(√c)
=√abc/(√a)+(√abc) /(√b)+(√abc) /(√c)
=√bc+√ac+√ab
只需证明:√bc+√ac+√ab=(√bc+√ac+√ab)^2
即:(a+b+c)>=(√bc+√ac+√ab) 当a/b=b/c=c/a 即a=b=c时取等号.
所以原式成立.
因为abc=1,原不等式等价于√ab+√ac+√bc<=a+b+c
等价于0<=(√a-√b)^2+(√a-√c)^2+(√b-√c)^2
显然成立