设x,y,z是实数,且(x-y)^2+(y-z)^2+(z-x)^2=(x+y-2z)^2+(y+z-2x)^2+(z+x-2y)_数学解答

设x,y,z是实数,且(x-y)^2+(y-z)^2+(z-x)^2=(x+y-2z)^2+(y+z-2x)^2+(z+x-2y)^2求[(xy+1)(yz+1)(zx+1)]/
[(x^2+1)(y^2+1)(z^2+x)]的值.

人气：280 ℃　时间：2019-10-23 11:23:56

解答

(x+y-2z)^2+(y+z-2x)^2+(z+x-2y)^2=((x-z)+(y-z))²+((y-x)+(z-x))²+((z-y)+(x-y))²=(x-z)²+(y-z)²+2(x-z)(y-z)+(y-x)²+(z-x)²+2(y-x)(z-x)+(z-y)²+(x-y)²+2(z-y)(x-y)...