X+4Y-3Z=0 (1)
4X-5Y+2Z=0 (2)
(1)*4-(2)
16Y-12Z+5Y-2Z=0
21Y=14Z
Y:Z=2:3
y=2z/3
(1)*5+(2)*4
5X-15Z+16X+8Z=0
21X=7Z
X:Z=1:3
x=z/3
不妨设z=6a,那么x=2a,y=3a,z=6a
（3x²+2xy+z²）/（x²+y²）= （12a²+12a²+36²）/（4a²+9a²）=72/13