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

a
b
)2的值.

lga+lgb=2
lga•lgb=
1
2

lg(ab)•(lg
a
b
)2

=(lga+lgb)(lga-lgb)2
=2[(lga+lgb)2-4lgalgb]
=2(4-4×
1
2
)=4