就是均值不等式啦.纯手打哦.应该没有算错.
∵条件a,b,c>0,1/a+1/b+1/c=1
∴a+2b+3c
=(a+2b+3c)[1/a+1/b+1/c]
=1+2+3+a/b+2b/a+a/c+3c/a+2b/c+3c/b
≥6+2[√2+√6+√3]
当且仅当a/b=2b/a,a/c=3c/a,2b/c=3c/b
a=√3c,a=√2b
∵1/a+1/b+1/c=1
∴1/a+√2/a+√3/a=1
∴a=1+√2+√3