由2x-3y-z=0,x+3y-14z=0,x≠0
解得y=3x/5 z=x/5
将y=3x/5 z=x/5 代入(x^3y+5xyz+xz)/(y^2+z^2)
(x^3y+5xyz+xz)/(y^2+z^2)
=(x^3*3x/5+5x*3x/5*x/5+x*x/5)/[(3x/5)^2+(x/5)^2]
=(3x^4/5+3x^3/5+x^2/5)/(9x^2/25+x^2/25)
=(3x^4/5+3x^3/5+x^2/5)/(2x^2/5)
=(3x^2+3x+1)/2
=3/2(x^2+x)+1/2
=3/2(x^2+x+1/4)+1/2-3/8
=3/2(x+1/2)^2+1/8
当x=-1/2时,(x^3y+5xyz+xz)/(y^2+z^2)的值最小,最小值为：1/8