已知A=x^3+3x^2y-5xy^2+6y^3-1,B=y^3+2xy^2+x^2y-2x^3+2,C=x^3-4x^2y+3xy^2-7y^3+1,求证A+B+C的值与x,y无关

来源：学生作业帮助网编辑：作业帮时间：2024/11/08 17:11:49

已知A=x^3+3x^2y-5xy^2+6y^3-1,B=y^3+2xy^2+x^2y-2x^3+2,C=x^3-4x^2y+3xy^2-7y^3+1,求证A+B+C的值与x,y无关
已知A=x^3+3x^2y-5xy^2+6y^3-1,B=y^3+2xy^2+x^2y-2x^3+2,C=x^3-4x^2y+3xy^2-7y^3+1,求证A+B+C的值与x,y无关

已知A=x^3+3x^2y-5xy^2+6y^3-1,B=y^3+2xy^2+x^2y-2x^3+2,C=x^3-4x^2y+3xy^2-7y^3+1,求证A+B+C的值与x,y无关
A+B+C
=(x^3+3x^2y-5xy^2+6y^3-1)+(y^3+2xy^2+x^2y-2x^3+2)+(x^3-4x^2y+3xy^2-7y^3+1)
=(x^3-2x^3+x^3)+(3x^2y+x^2y-4x^2y)+(-5xy^2+2xy^2++3xy^2)+(6y^3+y^3-7y^3)-1+2+1
=0+0+0+0+2
=2
所以A+B+C的值与x,y无关

你的有个向上的符号应该是开根的~~
这样就好解决咯，把A,B,C相加最终得到2，所以和X,Y 都没有关系啦！！

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