f(x1,x2,x3)=x1x2+x1x3+x2x3用配方法求标准型

二次型中不含平方项,故应先作一次坐标变换构造出平方项
令x1=y1+y2
x2=y1-y2
x3=y3
f=(y1+y2)(y1-y2)+(y1+y2)y3+(y1-y2)y3
=y1²-y2²+2y1y3
=y1²+2y1y3+y3²-y2²-y3²
=(y1-y3)²-y2²-y3²
∴标准型是：f=z1²-z2²-z3²