若xy∈R+ x+y=2 求证1/x+1/y≥2

Question

若xy∈R+ x+y=2 求证1/x+1/y≥2

Answer 1

(x+y)^2-(x-y)^2=4xy
=>
4>=4xy
=>
xy<=1
=>
(x+y)/xy>=2
=>
1/x+1/y>=2