已知x-y=2,x^2-y^2=12,求x与y的值

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已知x-y=2,x^2-y^2=12,求x与y的值已知x-y=2,x^2-y^2=12,求x与y的值已知x-y=2,x^2-y^2=12,求x与y的值解x-y=2①x²-y²=12

已知x-y=2,x^2-y^2=12,求x与y的值
已知x-y=2,x^2-y^2=12,求x与y的值

已知x-y=2,x^2-y^2=12,求x与y的值
解
x-y=2 ①
x²-y²=12
∴(x-y)(x+y)=12
即2(x+y)=12
∴x+y=6 ②
①+②得：
2x=8
∴x=4,y=2

x-y=2 (1)
x²-y²=12
∴x+y=(x²-y²)/(x-y)=12÷2=6 (3)
由（1），（3）解得
x=4, y=2

x^2-y^2=(x+y)(x-y)=12
∵x-y=2∴x+y=6
∴x=4 y=2

y=2 x=4

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