a,b是方程（lgx）^2-lgx^2-2=0的兩個根
即:
(lga)^2-2lga-2=0
(lgb)^2-2lgb-2=0
設m=lga,n=lgb
則:m^2-2m-2=0,n^2-2n-2=0
說明m,n是方程t^2-2t-2=0的二個根.
m+n=2,mn=-2
loga b+logb a=lgb/lga+lga/lgb=[(lgb)^2+(lga)^2]/(lga*lgb)
=[(m+n)^2-2mn]/(mn)
=[4-2*(-2)]/(-2)
=-4