解答题
17.用配方法化下列二次型为标准形：
f(x1，x2，x3)=x12+2x22一5x32+2x1x2—2x1x3+2x2x3．
f(x1，x2，x3)=x12+2x22一5x32+2x1x2—2x1x3+2x2x3．
【正确答案】令
则f(x1，x2，x3)=XTAX，
f(x1，x2，x3)=x12+2x22一5x32+2x1x2—2x1x3+2x2x3
=(x1+x2一x3)2+(x2+2x3)2一10x32，
且f(x1，x2，x3)
则f(x1，x2，x3)=XTAX，f(x1，x2，x3)=x12+2x22一5x32+2x1x2—2x1x3+2x2x3
=(x1+x2一x3)2+(x2+2x3)2一10x32，
且f(x1，x2，x3)
【答案解析】