Question

已知x.y属于正实数,且x+y+1/x+1/y=5,则x+y的最大值是

Answer 1

x+y+1/x+1/y =(x+y)(1+1/(xy)) 令x+y=k 4xy=1+4/k^2 所以 (x+y)(1+1/(xy))>=k(1+4/k^2)=k+4/k 也就是 k+4/k