Question

已知lga,lgb 是方程2x²-4x+1=0的两个根,则lgb分之a的平方等于多少

Answer 1

(lg b分之a)²

=[lg (a/b)]²

=(lg a-lgb)²

=(lga)²-2(lga)(lgb)+(lgb)²

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

=(lga+lgb)²-4(lga)(lgb)

=[-(-4/2)]²-4(1/2)

=4-2

=2