Question

若lga lgb是方程2x^2-4x+1=0的两个实根,求lg(ab)*lg(a/b)^2的值

Answer 1

根据二次方程根与系数的关系得 lga+lgb = 2 ,lga*lgb = 1/2 ,

那么可得 lg(ab) = lga+lgb = 2 ；

由于 [lg(a/b)]^2=(lga-lgb)^2 = (lga)^2+(lgb)^2-2lga*lgb = (lga+lgb)^2-4lga*lgb = 4-2 = 2 ,

所以,原式 = 2*2 = 4 .