令b/(a-3)=t
b=(a-3)t
所以 a²+2[(a-3)t]²=6
a²+2(a²t²-6at²+9t²)=6
(1+2t²)a²-12t²a+18t²-6=0
判别式=144t^4-4(1+2t²)(18t²-6)≥0
144t^4-4(18t²-6+36t^4-12t²)≥0
18t²-6-12t²≤0
6t²≤6
t²≤1
-1≤t≤1
所以 b/a-3的最大值为1