Question

运用公式 ）1：已知正数x y z满足x+2y+3z+6,求x2+1/2y2+1/3z2的最小值2：已知实数x y z满

Answer 1

1.x+2y+3z=6,

x2+y2/2+z2/3=x^2+(2x)^2/8+(3z)^2/27≥(x+2y+3z)^2/(1+8+27)(注：柯西不等式)

=36/36=1

∴x2+1/2y2+1/3z2的最小值为1

2.x+y+z=2

2x2+3y2+z2=x^2/(1/2)+y^2/(1/3)+z^2≥(x+y+z)^2/(1/2+1/3+1)=4/(11/6)=24/11

∴2x2+3y3+z2的最小值为24/11