Question

已知X-Y=A,Y-Z=B,求X方+Y方+Z方-XY-YZ-XZ的值

Answer 1

由X-Y=A与Y-Z=B相加得:

X-Z=A+B

原式=(X-Y)^2+2XY+Z^2-XY-YZ-XZ

=A^2+Z^2+XY-YZ-XZ

=A^2+Y(X-Z)+Z(Z-X)

=A^2+Y(X-Z)-Z(X-Z)

=A^2+(X-Z)(Y-Z)

=A^2+(A+B)B

=A^2+B^2+AB

答:X方+Y方+Z方-XY-YZ-XZ的值为A方+B方+AB.

有不懂的可以问我,请给个最佳,