Question

若实数XYZ 满足(X-Z)4(X-Y)(Y-Z)=0则下列式子一定成立的是

A . X Y Z =0 B. X Y - 2Z= 0 C . Y Z - 2X = 0 D . Z X - 2Y = 0 要过程，详细的

Answer 1

令 X-Y = a ,Y-Z = b ,
则 X-Z = (X-Y)+(Y-Z) = a+b ；
已知,(X-Z)²-4(X-Y)(Y-Z) = 0 ,
即有：(a+b)²-4ab = 0 ,
则有：(a-b)² = (a+b)²-4ab = 0 ,
可得：a-b = 0 ,
即有：(X-Y)-(Y-Z) = 0 ,
所以,Z+X-2Y = 0 ,
选 D .

Answer 2

设X-Y=a,Y-Z=b
由题意得 (a+b)^2-4ab=(a-b)^2=0
∴ a=b
∴ X-Y=Y-Z
∴ Z+X-2Y=0
∴选D