Question

若lga、lgb是方程x2-4x+1=0的两个根,求[lg(a/b)]^2的值

Answer 1

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