a+b=1,1/a+1/b=(a+b)(1/a+1/b)=2+(b/a+a/b)≥4(a+1/a)^2+(b+1/b)^2≥1/2[(a+1/a)+(b+1/b)]^2=1/2(a+b+1/a+1/b)^2≥1/2(1+4)=25/2