已知正数a,b,c满足1/a+1/b+1/c=1,证明:a/(1+a)+b/(1+b)+c/(1+c)大于等于9/4、
问题描述：
已知正数a,b,c满足1/a+1/b+1/c=1,证明:a/(1+a)+b/(1+b)+c/(1+c)大于等于9/4、
答
令1/a=x 1/b=y 1/c=z则x+y+z=1(1+x)+(1+y)+(1+z)=4 (1)a/(1+a)+b/(1+b)+c/(1+c)=1/(1/a+1)+1/(1/b+1)+1/(1/c+1) 变为1/(x+1)+1/(y+1)+1/(z+1)>=9/4 [1/(x+1)+1/(y+1)+1/(z+1)]((1+x)+(1+y)+(1+z))=1+(1+y)/(1+x)+(1+...