Question

已知 a>0,b>0,c>0,d>0求证(ad+bc)/bd + (bc+ad)/ac >=4

Answer 1

(ad+bc)/bd + (bc+ad)/ac=a/b +c/d +b/a +d/c=(a/b +b/a)+(c/d +d/c)>=2√[(a/b)(b/a)] +2√[(c/d)(d/c)]=2+2=4