已知正数a,b满足a2+b2=7ab.求证:lg a+b/3 =1/2(lg a +lg b )
问题描述:
已知正数a,b满足a2+b2=7ab.求证:lg a+b/3 =1/2(lg a +lg b )
答
a^2+2ab+b^2=9ab a+b=3√(ab) (a+b)/3=√(ab)
lg[(a+b)/3]=1/2(lga+lgb)