(√(ma+mb )^2=ma+nb (1)(m√(a）+n√(b）)^2=m^2a+n^2b+2mn√(ab) (2)(1)-(2)=a(m-m^2)+b(n-n^2)-2mn√(ab)=amn+bmn-2mn√(ab) =mn[a+b-2√(ab)]=mn[√(a)-√(b)]^2>=0=>√(ma+mb )^2>=[m√(a）+n√(b）]^2=>√(ma+...