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

来源：学生作业帮助网编辑：作业帮时间：2024/05/12 00:43:41

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

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

X+4Y-3Z=0和4X-5Y+2Z=0把Y当作常数来解出X,Z
X-3Z＝4Y，4X+2Z＝5Y。解得：X=14Y/16,Z=－11Y/16
代入算式：（3x²+2xy+z²）/(x²+y²)约去y就是：3(14/16)^2+2*14/16+(11/16)^2/[(14/16)^2+1]

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