已知a,b属于正实数,且a+b=1,求y=(a+a/1)(b+b/1)的最小值

(a+1/a)(b+1/b) =ab+b/a+a/b+1/(ab) =(a^2b^2+b^2+a^2+1)/(ab) =[a^2b^2+(a+b)^2-2ab+1]/(ab) =[a^2b^2+1-2ab+1]/(ab)=[(ab-1)^2+1]/(ab) 1=a+b>=2√(ab)所以√(ab)0所以0=25/4 当且仅当a=b=5/2时取等号,故(a+1/a)(b...