14(a2+b2+c2)=(a+2b+3c)2 14a2+14b2+14c2=a2+4ab+4b2+6ac+12bc+9c2 13a2+10b2+5c2-4ab-6ac-12bc＝0 (4a2-4ab+b2)+(9a2-6ac+c2)+(9b2-12bc+4c2)=0 (2a-b)2+(3a-c)2+(3b-2c)2=0 (2a-b)2=0, (3a-c)2=0, (3b-2c)2=0 2a-b=0, 3a-c=0, 3b-2c=0 2a=b , 3a=c, 3b=2c a:b=1:2 a:c=1:3 b:c=2:3 所以a:b:c=1:2:3
采纳哦