设1996x=1997y=1998z,xyz＞0,且√1996x+1997y+1998z=√1996+√1997+√1998,求1／x+1/y+1／z的值.
问题描述：
设1996x=1997y=1998z,xyz＞0,且√1996x+1997y+1998z=√1996+√1997+√1998,求1／x+1/y+1／z的值.
答
设1995x=1996y=1997z=k,显然k≠0,则1995=kx,1996=ky,1997=kz由已知得kx+ky+kz=3kx+3ky+3kz＞0,3k1x+1y+1z=3k1x+1y+1z,∵k≠0,∴31x+1y+1z=1x+1y+1z．∵xyz＞0,x,y,z同号,由已知得x＞0,y＞0,z＞0,∴1x+1y+1z=1...