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

Answer 1

【题中(X-Z)少了平方,否则当X=3/2、Y=3/4、Z=3/8时满足题意,但ABCD都不成立】

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 .