已知X,Y,Z爲三個互不相等的數,且X+ 1/Y =Y+ 1/Z = Z+ 1/X.求證:(XYZ)^2 = 1
題目:
已知X,Y,Z爲三個互不相等的數,且X+ 1/Y =Y+ 1/Z = Z+ 1/X.求證:(XYZ)^2 = 1
解答:
由 X+1/Y=Y+1/Z 得ZY=(Y-Z)/(X-Y) 同理有XZ=(Z-X)/(Y-Z);XY=(Y-X)/(X-Z) 因此(XYZ)~2=zy*xz*xy=1
題目:
已知X,Y,Z爲三個互不相等的數,且X+ 1/Y =Y+ 1/Z = Z+ 1/X.求證:(XYZ)^2 = 1
解答:
由 X+1/Y=Y+1/Z 得ZY=(Y-Z)/(X-Y) 同理有XZ=(Z-X)/(Y-Z);XY=(Y-X)/(X-Z) 因此(XYZ)~2=zy*xz*xy=1
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