已知X2+Y2=1,求XY/X+Y的最大值

Question

已知X2+Y2=1,求XY/X+Y的最大值

Answer 1

解;已知x,y满足,x2+y2=1则1=x2+y2≥2xy∴xy≤1/2 ①xy/(x+y)=1/(1/x+1/y)≤1/ [2√(1/x•1/y)]=√(x•y)/2②①②xy/(x+y) ≤√(1/2)/2 =√2/4当且仅当①②同取等号,即x=y=√2/2取max√2/4...