Question

已知方程组{（x+y)-3(x-y)=7 {2(x+y)+(x-y)=0 则x的平方-y的平方的值为

写出理由，一定家悬赏

Answer 1

解：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

Answer 2

把x+y，x-y分别看成两个未知数，把已知方程组看做是关于x+y，x-y的二元一次方程组。

(x+y)-3(x-y)=7 (1)
2(x+y)+(x-y)=0 (2)
(2)-(1)×2
7(x-y)=-14
x-y=-2
(2)×3+(1)
7(x+y)=7
x+y=1

x^2-y^2
=(x+y)(x-y)
=-2

Answer 3

(x+y)-3(x-y)=7 4y-2x=7
2(x+y)+(x-y)=0 3x-y=0
x=0.7 y=2.1
x^2-y^2=(x+y)(x-y)=-1.4*2.8=-3.92

Answer 4

SB 老师不是讲过了吗……BS