已知3x-2y-5z=0,2x-5y+4z=0,且x.y.z均不为0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2的值

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已知3x-2y-5z=0,2x-5y+4z=0,且x.y.z均不为0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2的值
已知3x-2y-5z=0,2x-5y+4z=0,且x.y.z均不为0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2的值

已知3x-2y-5z=0,2x-5y+4z=0,且x.y.z均不为0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2的值
3x-2y-5z=0 12x-8y-20z=0
2x-5y+4z=0 10x-25y+20z=0
两式相加
22x-33y=0
22x=33y
y=2/3x
3x-2y-5z=0 15x-10y-25z=0
2x-5y+4z=0 4x-10y+8z=0
两式相减
11x-33z=0
11x=33z
z=1/3x
3x^2+2y^2+5z^2/5x^2+y^2-9z^2
=(3x^2+8/9x^2+5/9x^2)/(5x^2+4/9x^2-x^2)
=(40/9)/(40/9)
=1

通过方程合并联立:x=3z;y=2z,结果=1