已知X+4Y+3X=3X-2Y-5Z=0(XYZ不等于0),求XY+YZ+2XZ/2XX-3YY+7ZZ的值
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已知X+4Y+3X=3X-2Y-5Z=0(XYZ不等于0),求XY+YZ+2XZ/2XX-3YY+7ZZ的值
X+4Y+3Z=0
X-2Y-5Z=0
解方程组得:x=7z/3,y=-4z/3
代入:
XY+YZ+2XZ/2XX-3YY+7ZZ
=(7z/3*(-4z/3)-4z/3*z+2*7z/3*z)/(2*(7z/3)^2-3*(-4z/3)^2+7z^2)
=(-28z^2/9-4z^2/3+14z^2/3)/(98z^2/9-16z^2/3+7z^2)
=(2z^2/9)/(113z^2/9)
=2/113
X-2Y-5Z=0
解方程组得:x=7z/3,y=-4z/3
代入:
XY+YZ+2XZ/2XX-3YY+7ZZ
=(7z/3*(-4z/3)-4z/3*z+2*7z/3*z)/(2*(7z/3)^2-3*(-4z/3)^2+7z^2)
=(-28z^2/9-4z^2/3+14z^2/3)/(98z^2/9-16z^2/3+7z^2)
=(2z^2/9)/(113z^2/9)
=2/113
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