Question

证明：(X+Y-2Z)的三次方+ (Y+Z-2X) 的三次方 +（Z+X-2Y)的三次方 =3（X+Y-2Z）（Y+Z-

Answer 1

为书写简明,设

x-z=a,y-z=b,x-y=c

左边=(X+Y-2Z)^3+ (Y+Z-2X)^3 +（Z+X-2Y)^3

=(a+b)^3-(c+a)^3+(c-b)^3

=a^3+3a^2b+3ab^2+b^3-(a^3+3a^2c+3ac^2+c^3)+c^3-3c^2b+3cb^2-b^3

=3a^2b+3ab^2-3a^2c-3ac^2-3c^2b+3cb^2

=3(a^2b+ab^2-a^2c-ac^2-c^2b+cb^2)

=3[a^2(b-c)+a(b+c)(b-c)+bc(b-c)]

=3(b-c)(a^2+ab+ac+bc)

=3(b-c)(a+c)(a+b)

=-右边.

解了半天,结果出现相反数.

供你参考吧.