已知x=1/2a+1,y=1/2a+2,z=a-3,求x^2+2xy+y^2-2xz+z^2-2yz的值.

问题描述:

已知x=1/2a+1,y=1/2a+2,z=a-3,求x^2+2xy+y^2-2xz+z^2-2yz的值.

x^2+2xy+y^2-2xz+z^2-2yz=(X+Y)^2+Z(z-2x-2y)=(X+Y)^2+Z[z-2(x+y)]=(1/2a+1+1/2a+2)^2+(a-3)[a-3-2(1/2a+1+1/2a+2)]=(a+3)^2+(a-3)[a-3-2(a+3)]=(a+3)^2+(a-3)(-a-9)=a^2+6a+9-a^2-6a+27=36