根据柯西不等式：[1²+(1/√2)²+(1/√3)²][X^2+（√2Y)²+(√3Z)²]≥(x+y+z)²∴(x+y+z)²≤(1+1/2+1/3)*(x²+2y²+3z²)=11/6*18=33∴x+y+z≤√33∴X+Y+Z的最大值为√33
