1) a>0,b>0 ab>01/(a +1) +1/(b+ 1)=(a+b+2)/(ab+a+b+1)=3/(2+ab)0,b>0a+b>2√ab,(a^2+b^2)/(a+b)=a+b-2ab/a+b≥2√ab-2ab/(2√ab)=√ab(a^2+b^2)/√ab≥a+b