1.已知
求(X^2+Y^2+Z^2)/(XY+YZ+2XZ)
3X-4Y-2Z=0.(1)
2X-Y-8Z=0 .(2)
(1)*4-(2)
10X-15Y=0
X=3Y/2
Z=Y/4
(X^2+Y^2+Z^2)/(XY+YZ+2XZ)
=(9Y ^2/4+Y^2+Y^2/16)/[3Y^2/2+Y^2/4+2*(3Y/2)*(Y/4)]
=53/40
答：(X^2+Y^2+Z^2)/(XY+YZ+2XZ)=53/40
2.已知ABC=1.求1/(AB+A+1)+1/(BC+B+1)+1/(CA+C+1)的值
1/(AB+A+1)+1/(BC+B+1)+1/(CA+C+1)
=1/(AB+A+ABC)+1/(BC+B+1)+1/(CA+C+1)
=1/[A*(BC+B+1)]+1/(BC+B+1)+1/(CA+C+1)
=（1+A）/[A*(BC+B+1)]+1/(CA+C+1)
=（1+A）/(AB+A+1)+1/(CA+C+1)
=[（1+A）*(CA+C+1)+(AB+A+1)]/[(AB+A+1)*(CA+C+1)]
=（2AC+2A+2+C+CA^2+AB）/（2AC+2A+2+C+CA^2+AB）
=1
答：1/(AB+A+1)+1/(BC+B+1)+1/(CA+C+1)=1
3.已知3A^2+AB-2B^=0,求代数式A/B-B/A-(A^2+B^2)/（AB）的值...
3A^2+AB-2B^=0
（3A-2B）*（A+B）=0
B/A=3/2或B/A=-1
A/B-B/A-(A^2+B^2)/（AB）
=A/B-B/A-A/B-B/A
=-2B/A
=-3或=2
答：A/B-B/A-(A^2+B^2)/（AB）=-3或=2