设2X-3Y-Z=0,X+3Y-14Z=0,X≠0,求x^3y+5xyz+xz/y^2+z^2的最小值.

问题描述:

设2X-3Y-Z=0,X+3Y-14Z=0,X≠0,求x^3y+5xyz+xz/y^2+z^2的最小值.

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)=(3...