已知方程组{(X+Y)-3(X-Y)=7,2(X+Y)+(X-Y)=-7}则(X+Y)(X-Y)=

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已知方程组{(X+Y)-3(X-Y)=7,2(X+Y)+(X-Y)=-7}则(X+Y)(X-Y)=已知方程组{(X+Y)-3(X-Y)=7,2(X+Y)+(X-Y)=-7}则(X+Y)(X-Y)=已知

已知方程组{(X+Y)-3(X-Y)=7,2(X+Y)+(X-Y)=-7}则(X+Y)(X-Y)=
已知方程组{(X+Y)-3(X-Y)=7,2(X+Y)+(X-Y)=-7}则(X+Y)(X-Y)=

已知方程组{(X+Y)-3(X-Y)=7,2(X+Y)+(X-Y)=-7}则(X+Y)(X-Y)=
设x+y=m,x-y=n.则:已知的方程组变为:m-3n=7,2m+n=0,解这个新的方程组得:m=1,n=-2所以:x²-y²=(x+y)(x-y)=mn=-2

设x+y=m,x-y=n。
则:已知的方程组变为:
m-3n=7,2m+n=-7,
解这个新的方程组得:
m=-2,n=-3
(X+Y)(X-Y)=-2*(-3)=6

设x+y=m,x-y=n。则:已知的方程组变为:m-3n=7,2m+n=0,
解这个新的方程组得:m=1,n=-2
所以:x²-y²=(x+y)(x-y)=mn=-2

设x+y=m,x-y=n。则:已知的方程组变为:m-3n=7,2m+n=0,
解这个新的方程组得:m=1,n=-2
所以:(x+y)(x-y)=x²-y²=mn=-2

(X+Y)-3(X-Y)=7①
2(X+Y)+(X-Y)=-7②
①+②×3
7(x+y)=7-21
(x+y)=-2
∴(x-y)=-3

(X+Y)(X-Y)=(-2)×(-3)=6