如果x-y=6,xy=7,那么x^2-y^2=?

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如果x-y=6,xy=7,那么x^2-y^2=?

如果x-y=6,xy=7,那么x^2-y^2=?

x-y=6(1),xy=7,(2)
由(1)得 y=6+x(3)
把(3)带入(2)的
x(6+x)=7
解得x=1或者x=-7
x=1 时y=7 或者x=-7时 y=1
x^2-y^2=-48或者48

(x+y)^2=(x-y)^2+4xy=64 x+y=8或-8 x^2-y^2=48或-48

x-y=6,则(x-y)²=6²=36
(x+y)²=(x-y)²+4xy=36+4×7=64
所以x+y=8或-8
x^2-y^2=(x+y)(x-y)=6(x+y)=±48
所以x^2-y^2等于48或-48

(x+y)^2=(x-y)^2+4xy=36+4×7=64
所以x+y=8或-8
x^2-y^2=(x+y)(x-y)=±48

X=7,y=1结果等于48

x-y=6,xy=7
(x+y)^2=(x-y)^2+4xy=36+4*7=64
x+y=±8
x^2-y^2=(x+y)(x-y)= ±8*6=±48

x^2-y^2=(x-y)(x+y)
x+y=根号(x+y)^2=根号(x^2-2xy+y^2+4xy)=根号(36+4*7)=正负8
x^2-y^2=正负48

x=7,y=1,x^2-y^2=49-1=48

(x+y)^2=(x-y)^2+4xy=64 x+y=8或-8 x^2-y^2=48或-48