若a/x^2-yz=b/y^2-zx=c/z^2-xy,求证ax+by+cz=(a+b+c)(x+y+z)

若a/x^2-yz=b/y^2-zx=c/z^2-xy,求证ax+by+cz=(a+b+c)(x+y+z) y^2+yz+z^2=a^2,z^2+zx+x^2=b^2,yz+zx+xy=0.证明:(a+b+c)(a+b-c)(a-b+c)(a-b-c)=10y^2+yz+z^2=a^2,yz≥0 z^2+zx+x^2=b^2,zx≥0 x^2+xy+y^2=c^2,xy≥0 yz+zx+xy=0,x＝y＝z＝0 (a+b+c)(a+b-c)(a-b+c)(a-b-c)=0 y^2+yz+z^2=a^2,yz≥0 z^2+zx+x^2=b^2,zx≥0 x^2+x 若x+y+z=a,xy+yz+zx=b,xyz=c,则xy^2+x^2y+yz^2+y^2z+xz^2+x^2z=? a/x^2-yz=b/y^2-zx=c/z^2-xy xyz=0 求证ax+by+cz=(a+b+c)(x+y+z) 已知a,b,c,x,y,z都是正数,求(b c)/ax^2 (c a)/by^2 (a b)/cz^2>=2(xy yz zx) 若x,y,z属于R,a,b,c属于R+,求证：[(b+c)/a]x^2+[(c+a)/b]y^2+[(a+b)/c]z^2>=2(xy+yz+zx) 二个数学证明题1.证明：x+y 4 已知：---------- >= ------- 证明：xy(4-xy) 4+x+yx+y y+z z+x---------+ ---------- + ---------- >=2xy(4-xy) yz(4-yz) zx(4-zx)a b c2证明：若a,b,c属于R+,证明：------- + -------- + -------- >= 1b+2c c+2 已知:x+y+z=a,xy+yz+zx=b,则x^2+y^2+z^2等于多少. y^2+yz+z^2=a^2,z^2+zx+x^2=b^2,x^2+xy+y^2=c^2,yz+zx+xy=0.证明:(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0 y^2+yz+z^2=a^2,z^2+zx+x^2=b^2,x^2+xy+y^2=c^2,yz+zx+xy=0.证明:(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0 已知非零实数xyz满足xy=a,yz=b,zx=c,则x^2+y^2+z^2的值为 实数a.b.c满足x+y+z=5,xy+yz+zx=3,求z的最大值 a/x*x-yz=b/y*y-zx=c/z*z-xy求证ax+by+cz=(x+y+z)*(a+b+c) 1=xy/x+y,2=yz/y+z,3=zx/z+x,则x+y+z的值为（ ）.A.276/35 B.-276/35 C.11/12 D.-11/12 已知x-y=a,x-y=10,则代数式x^2+y^2+z^2-xy-yz-zx的最小值等于（ ）. A.75 B.80 C.100 D.105打错题目了，抱歉。已知x-y=a,z-y=10,则代数式x^2+y^2+z^2-xy-yz-zx的最小值等于（ ）. A.75 B.80 C.100 D.105 几道奥数计算题1/（a-b)+1/（a+b)+2a/(a^2+b^2)+(4a^3)/(a^4+b^4)=?[(x^2+yz)/(x^2+(y+z)-yz)]+[(y^2-zx)/(y^2+(z+x)y+zx)]+[(z^2+xy)/(z^2-(x-y)z-xy]会多少写多少 xy 2yz 3zx 4xyz________ = ________ = _______ = ___________ (xyz不等于0)x+y+xy y+z+yz z+x+zx xy+yz+zx最好有解题思路 算出 X Y Z 分别等于几 分式题:xy=x+y,yz=2(y+z),zx=3(z+x),求xyz/(xy+yz+xz)xy=x+y,yz=2(y+z),zx=3(z+x),求xyz/(xy+yz+xz)