已知a,b,c为正数,求证（a+b+c)(1/a+1/(b+c)＞＝4

Question

已知a,b,c为正数,求证（a+b+c)(1/a+1/(b+c)＞＝4

Answer 1

（a+b+c)(1/a+1/(b+c)=1+ (b+c)/a + 1+ a/(b+c)
>= 2+ 2*根号{[(b+c)/a]*[a/(b+c)]} =4