因为1/X+9/Y=1而1=1/X+9/Y≥2√(9/XY)√(XY)≤6又因为X+Y≥2√(XY)=2*6=12当且仅当X=Y时取等号所以X+Y的最小值=12
1/x+9/y=1=> x=y/(y-9)x+y=y/(y-9)+y=(y^2-8y)/(y-9)=((y-9)^2+10(y-9)+9)/(y-9)=y-9+9/(y-9)+10>=2根号((y-9)*9/(y-9))+10=16此时y=12 x=4