Question

x^4-y^4-4x^2+4y^2=0

x^4-y^4-4x^2+4y^2=0 化解

Answer 1

x^4-y^2-4x^2+4y^2=0
(x^2-y^2)(x^2+y^2)-4(x^2-y^2)=0
这一步利用了平方差公式
然后提取公因式，得：
(x^2-y^2)(x^2+y^2-4)=0
(x-y)(x+y)(x^2+y^2-4)=0

Answer 2

x^4-y^4-4x^2+4y^2=0
(x^2-y^2)(x^2+y^2)-4(x^2-y^2)=0
(x^2-y^2)(x^2+y^2-4)=0
(x+y)(x-y)(x^2+y^2-4)=0

所以 x=y 或 x=-y 或 x^2+y^2=4

Answer 3

x^4-y^4-4x^2+4y^2=0
(x²+y²)(x²-y²)-4(x²-y²)=0
(x²+y²-4)(x²-y²)=0
(x²+y²-4)(x+y)(x-y)=0

Answer 4

x^4-y^2-4x^2+4y^2=0
(x²-y²)(x²+y²)-4(x²-y²)=0
(x²-y²)(x²+y²-4)=0
(x-y)(x+y)(x²+y²-4)=0
(x-y)(x+y)(x²+y²-4)=0

所以x=y或 x=-y 或x²+y²=4