实数x,y,z满足(x-z)的平方减4(x-y)(y-z)=0求证z+x-2y=0

问题描述:

实数x,y,z满足(x-z)的平方减4(x-y)(y-z)=0求证z+x-2y=0

原式=(x-z)∧2-4(x-y)(y-z)=(x-y+y-z)∧2-4(x-y)(y-z)=(x-y)∧2+(y-z)∧2+2(x-y)(y-z)-4(x-y)(y-z)=(x-y)∧2+(y-z)∧2-2(x-y)(y-z)=[(x-y)-(y-z)]...