Question

若x,y都是正数,且xy=x+y+4,则xy的取值范围是

Answer 1

x,y都是正数,x+y≥2√xy

设xy=t

t=x+y+4≥2√t+4

t-2√t-4≥0 (√t-1)^2≥5

√t≥1+√5 t≥6+2√5