已知方程组x+2y-z=0,2x-y+8z=0,求xx+yy+z*z/xy+yz的值

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已知方程组x+2y-z=0,2x-y+8z=0,求x*x+y*y+z*z/xy+yz的值
已知方程组x+2y-z=0,2x-y+8z=0,求x*x+y*y+z*z/xy+yz的值

已知方程组x+2y-z=0,2x-y+8z=0,求x*x+y*y+z*z/xy+yz的值
x+2y-z=0,2x-y+8z=0,
可知
x=-3z y=2z
所以
x*x+y*y+z*z/xy+yz
=(9z^2+4z^2+z^2)/(-6z^2+2z^2)
=(14z^2)/(-4z^2)
=-7/2

把未知数的倍数调一致两式相减

由x+2y-z=0,2x-y+8z=0得x=-3z,y=2z
故x*x+y*y+z*z/xy+yz=9z^2+4z^2+z^2/(-6z^2)+2z^2=15z^2-1/6

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