Question

若x>1 y>1 不等式lg(xy)

Answer 1

设lgx=m,lgy=n,则m>0,n>0.m＋n≤(lga)√(m²＋n²),lga≥【(m＋n)/√(m²＋n²)】的最大值.(m＋n)/(m²＋n²)=√[(m²＋2mn＋n²)/(m²＋n²)]=√[1＋(2mn)/(m²＋n²)≤√[1＋1]=√2,lga≥√2,a≥10^(√2)