Question

已知x,y∈（-√3,√3）,且xy=-1 ,求s=3/(3-x^2)+12/(12-y^2)的最小值

Answer 1

12/5

提示：将y=-1/x代入化简得

s=1-(35x^2)/(12x^4 - 37x^2+3),

由xy=-1知x≠0,从而x^2>0,

s=1-(35)/(12x^2+3/x^2 - 37 )

≥1-35/(2√36 -37)=12/5,

当且仅当12x^2=3/x^2=6,即x=±√2/2时,s有最小值12/5.