令A:a=1:m,則A=L /(1+m) ,a=mL /(1+m),m>0
B:b=1:n,則B=L /(1+n), b=nL /(1+n),n>0
C:c=1:t,則C=L /(1+t), c=tL /(1+t), t>0
aB+cA+bC
=mL^2/[(1+m)(1+n)] + tL^2/[(1+m)(1+t)]+ nL^2/[(1+n)(1+t)]
=[(m+n+t+mn+nt+mt)/(1+m+n+t+mn+nt+mt+mnt)]*L^2<L^2,得證
不知這算不算第三種證法?
可否分享一下您已知的兩種證法?