若lga、lgb是方程2x2-4x+1=0的两个实根,求lg(ab)•(lga/b)2的值.
问题描述:
若lga、lgb是方程2x2-4x+1=0的两个实根,求lg(ab)•(lg
)2的值. a b
答
,
lga+lgb=2 lga•lgb=
1 2
lg(ab)•(lg
)2a b
=(lga+lgb)(lga-lgb)2
=2[(lga+lgb)2-4lgalgb]
=2(4-4×
)=41 2