证明：(x+y)/(1+x)(1+y)≥2√(xy)/(1+√(?
证明：(x+y)/(1+x)(1+y)≥2√(xy)/(1+√(xy))^2，其中等号当且仅当x＝y时取得。
(x+y)/(1+x)(1+y)≥2√(xy)/(1+√(xy))^2 →(x+y)/(1+x+y+xy)≥2√xy/(1+xy+2√xy) →(1+x+y+xy)/(x+y)≤(1+xy+2√xy)/(2√xy) →(1+xy)/(x+y)≤(1+xy)/(2√xy) →x+y≥2√xy. 当且仅当x＝y时取得等号.