因为
lga、lgb是方程x2-4x+1=0的两个根,
所以
lga+lgb=4,lga*lgb=1
从而
[lg(a/b)]^2=(lga-lgb)^2
=(lga+lgb)^2-4lga*lgb
=4^2-4*1
=16-4
=12