1.已知3x-4y-z=0,2x+y-8z=0,求x^2+y^2+z^2/xy+yz+xz的值.2.已知關于X的方程a(x-3)+b(3x+1)=5x+1有無窮多個解，求a,b的值。

熱心網友

1、3x-4y-z = 0 (1), 2x+y-8z = 0 (2)由(1)得：z = 3x-4y, 代入（2)得：2x+y-24x+32y = 0, x = 3y/2, z = 3x-4y = y/2x^2+y^2+z^2 = (9/4+1+1/4) = 3.5y^2, xy+yz+zx = (3/2+1/2+3/4)y^2 = 2.75y^2x^2+y^2+z^2/xy+yz+xz = 3.5/2.75 = 14/112、左邊 = (a+3b)x + (b-3a), a(x-3)+b(3x+1)=(a+3b)x + (b-3a) = 5x+1有無窮多個解當且僅當a+3b = 5, b-3a = 1, 解得a=0.2 b=1.6