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已知X+4Y-3Z=0,4X-5Y+2Z=0,xyz≠0,求X方+Y方分之3X方+2XY+Z方
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已知X+4Y-3Z=0,4X-5Y+2Z=0,xyz≠0,求X方+Y方分之3X方+2XY+Z方
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答案和解析
X+4Y-3Z=0 (1)
4X-5Y+2Z=0 (2)
4X+16Y-12Z=0 (3)
(3)-(2)得
21Y-14Z=0
Y=2/3Z
X=1/3Z
∵XYZ≠0
∴（3X^2+2XY+Z^2）/(X^2+Y^2)=16/5
4X-5Y+2Z=0 (2)
4X+16Y-12Z=0 (3)
(3)-(2)得
21Y-14Z=0
Y=2/3Z
X=1/3Z
∵XYZ≠0
∴（3X^2+2XY+Z^2）/(X^2+Y^2)=16/5
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