求证：((a-b)(b+c))/(c-a)+((a+c)(b-c))/(a-b)+((a+b)(c-a))/(b-c)=0
求证：((a-b)(b+c))/(c-a)+((a+c)(b-c))/(a-b)+((a+b)(c-a))/(b-c)=0
日期：2022-02-07 10:47:21 人气：1
设：x=a+b，y=b+c，z=a+c
可得a-b=z-y，b-c=x-z，c-a=y-x
原式= (z-y)/x+(x-z)/y + (y-x)/z+(z-y)(x-z)(y-x)/(xyz)
= (yz-y²+x²-zx)/(xy) + (y-x)[xy+(z-y)(x-z)]/(xyz)
= (x-y
可得a-b=z-y，b-c=x-z，c-a=y-x
原式= (z-y)/x+(x-z)/y + (y-x)/z+(z-y)(x-z)(y-x)/(xyz)
= (yz-y²+x²-zx)/(xy) + (y-x)[xy+(z-y)(x-z)]/(xyz)
= (x-y