整数x ,y,z满足(x-y)(y-z)(z-x)=x+y+z.证明:x+y+z能被27整除

设X,Y,Z都是整数,满足条件(X-Y)(Y-Z)(Z-X)=X+Y+Z,试证明X+Y+Z能被27整除 (x+y-z)(x-y+z)= x,y,z正整数 x>y>z证明 x^2x +y^2y+z^2z>x^(y+z)*y^(x+z)*z^(x+y) 设x、y、z为整数,证明:x^4*(y-z)+y^4*(z-x)+z^4*(x-y)/(y+z)^2+(z+x)^2+( 证明:x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2能被(x+y+z)整除 试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y) X+Y+Z=? 已知x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求代数式x2/(y+z)+y2/(x+z)+z2/ 已知实数x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求x2/(y+z)+y2/(z+x)+z2/( 若整数x，y，z满足(98) f(x,y,z,w)=x*(x+y)*(x+y+z)*(x+y+z+w) (y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z