用配方法化二次型为标准型f(X1,x2,x3)=2x1x2-4x1x3+2x2^2-2x2x3
问题描述：
用配方法化二次型为标准型f(X1,x2,x3)=2x1x2-4x1x3+2x2^2-2x2x3
答
f= (2x2^2+2x1x2-2x2x3)-4x1x3
= 2(x2+x1/2-x3/2)^2 - (1/2)x1^2 -(1/2)x3^2-3x1x3
= 2(x2+x1/2-x3/2)^2 - (1/2)(x1+3x3)^2 +4x3^2