Question

已知x＞1＞y,且x/(x-1)+y/(1-y)=1,则x-y的最小值?

Answer 1

先对x/(x-1)+y/(1-y)=1通分,可得（x-xy+xy-y）/(x-1)(1-y)=1,整理后可得出xy+1-2y=0,进一步可得x=2-1/y.所以x-y=2-1/y-y,设f（y）=2-1/y-y,对其求导f'(y)=1/y²-1,设f'(y)=0,y=1或-1,结合x>1>y,所以y=-1,所以有

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