a＾2+b＾2+c＾2+42＜ab+9b+8c
a^2+b^2+c^2-ab-9b-8c+42<0
(a-1/2b)^2+(√3b/2-3√3)^2+(c-4)^2+42-(3√3)^2-4^2<0
(a-1/2b)^2+(√3b/2-3√3)^2+(c-4)^2-1<0
(a-1/2b)^2+(√3b/2-3√3)^2+(c-4)^2<1
∵a,b,c为正整数
∴c-4=0
√3b/2-3√3=0
a-1/2b=0
c=4
b=6
a=3