初一数学已知3x-4y-z=0,2x+y-8z=0,且x,y,z不全为0求x²+2xy+z²/xy+yz+zx的值

问题描述:

初一数学已知3x-4y-z=0,2x+y-8z=0,且x,y,z不全为0求x²+2xy+z²/xy+yz+zx的值

由题中两等式可得x=3z ,y=2z
代入所求多项式
(3z)^2+2*3z*2z+(z^2)/(2z*3z)+2z*z+3z*z=26z^2+1/6

3x-4y-z=0 2x+y-8z=08x+4y-32z=0 3x-4y-z+8x+4y-32z=011x-33z=0x=3z y=2z x²+2xy+z²/xy+yz+zx=(3z)^2+12z^2+z^2/6z^2+2z^2+3z^2=9z^2+12z^2+z^2/6z^2+2z^2+3z^2=22z^2/11z^2=2