实数x,y满足[√(x2+1997)-x][√(y2+1997)-y]=1997求x+y的值.

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因为[√(x2+1997)-x][√(y2+1997)-y]=1997
所以√(x2+1997)-x=1997/[√(y2+1997)-y]=1997*[√(y2+1997)+y]/1997=√(y2+1997)+y
所以x+y=√(x2+1997)-√(y2+1997)
同理
√(y2+1997)-y=1997/[√(x2+1997)-x]=1997[√(x2+1997)-x]/1997=√(x2+1997)+x
所以x+y=√(y2+1997)-√(x2+1997)
x+y=0

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