已知X+4Y-3Z=0,4X-5Y+2Z=0(XYZ≠0),求（3x²+2xy+z²）/(x²+y&_数学解答

已知X+4Y-3Z=0,4X-5Y+2Z=0(XYZ≠0),求（3x²+2xy+z²）/(x²+y²)的值,

人气：495 ℃　时间：2019-08-16 22:05:18

解答

X+4Y-3Z=0 (1)
4X-5Y+2Z=0 (2)
(1)*4-(2),得：3Y=2Z
(1)*2-(2)*3,得：2X=Y
把Z=3/2 Y,X=1/2 Y 带入式（3x²+2xy+z²）/(x²+y²),解得为16/9