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
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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
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
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
分子与分母反转,分式仍相等.所以
1/y+1/x+1=(1/2)(1/z+1/y+1)=(1/3)(1/x+1/z+1)=(1/4)(1/z+1/x+1/y)
令四个代数值分别=A,则
1/x+1/y=A-1
1/y+1/z=2A-1
1/z+1/x=3A-1
1/x+1/y+1/z=4A
由此,(1)(3)式相加,得
1/x+1/x+1/y+1/z+2=4A=1/x+1/y+1/z,1/x+2=0,1/x=-2,x=-1/2;
(1)式乘以2加(2)式得
1/x+1/y+1/x+1/y+1/y+1/z+3=4a=1/x+1/y+1/z,2/y=-1,y=-2;
(1)式乘以4减(4)式得
3*(1/x+1/y)-1/z=-1,1/z=3*(-2-1/2)+1=-13/2,z=-2/13.
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
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