Question

若lga，lgb是方程2x²-4x+1=0的兩個根，則(lg

a

b

)2=______．

Answer 1

∵lga，lgb是方程2x²-4x+1=0的兩個根，∴lga+lgb=2，lga•lgb=

1

2

，
∴(lg

a

b

)2=（lga-lgb）²=（lga+lgb）²-4lga•lgb=4-4×

1

2

=2，
故答案為 2．