已知x,y,z均为实数,且满足:x+2y-z=6,x-y+2z=3.求x+y+z的最小值_数学解答

已知x,y,z均为实数,且满足:x+2y-z=6,x-y+2z=3.求x+y+z的最小值

人气：154 ℃　时间：2020-01-15 20:53:50

解答

x+2y-z=6,.(1) x-y+2z=3.(2) (1)-(2) y-z=1,y=1+z (1)+2(2) x+z=4,x=4-z x^2+y^2+z^2=(4-z)^2+(1+z)^2+z^2 =3z^2-6z+17=3(z-1)^2+14 当z=1,最小值=14