线性代数初级问题证明|y+z z+x x+y| |x y z||x+y y+z z+x| = 2|z x y||z+x

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) (x+y-z)(x-y+z)= 试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y) (y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z X+Y+Z=? 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(x-2z+y)(y+z-2x)+(x 已知 x,y,z都是正实数,且 x+y+z=xyz 证明 (y+x)/z+(y+z)/x+(z+x)/y≥2(1/x+1 ①(x+y+z）（-x+y+z）(x-y+z)(x+y-z) 数学 多项式(x+y-z)(x-y+z)-(y+z-x)(z-x-y)公因式 方向 X Y Z (x+y+z)^5-(x+y-z)^5-(x+z-y)^5-(z+y-x)^5, 如何化简(x+y+z)(x+y-z)(x-y+z)(-x+y+z)