已知4X-3Y-3Z=0和X-3Y-Z=0 X:Y:Z的值
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已知4X-3Y-3Z=0和X-3Y-Z=0 X:Y:Z的值
4X-3Y-3Z=0(1)
X-3Y-Z=0 (2)
(1)-(2),
3x=2z,x=2z/3,(3)
(3)代人(2),
y=-z/9,
所以x:y:z=(2z/3):(-z/9):z=(2/3):(-1/9):1=6:(-1):9
(xy+2yz)/(x^2+y^2-z^2)
=[(2z/3)(-z/9)+2(-z/9)*z]/[(2z/3)^2+(-z/9)^2+z^2]
=(2z^2/27-2z^2/9)/(4z^2/9+z^2/81+z^2)
=(-4/27)/(118/81)
=-6/59
X-3Y-Z=0 (2)
(1)-(2),
3x=2z,x=2z/3,(3)
(3)代人(2),
y=-z/9,
所以x:y:z=(2z/3):(-z/9):z=(2/3):(-1/9):1=6:(-1):9
(xy+2yz)/(x^2+y^2-z^2)
=[(2z/3)(-z/9)+2(-z/9)*z]/[(2z/3)^2+(-z/9)^2+z^2]
=(2z^2/27-2z^2/9)/(4z^2/9+z^2/81+z^2)
=(-4/27)/(118/81)
=-6/59
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