若x+y=3m,x-y=n/3,则x^4+y^4-2x^2y^2=

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 13:26:47
若x+y=3m,x-y=n/3,则x^4+y^4-2x^2y^2=

若x+y=3m,x-y=n/3,则x^4+y^4-2x^2y^2=
若x+y=3m,x-y=n/3,则x^4+y^4-2x^2y^2=

若x+y=3m,x-y=n/3,则x^4+y^4-2x^2y^2=
x^4+y^4-2x^2y^2=(x²-y²)²=(x-y)²(x+y)²=m²n²

x^4+y^4-2x^2y^2=(x^2-y^2)^2=[(x+y)(x-y)]^2
=(3m*n/3)^2=(mn)^2=m^2n^2

(X+Y)*(X-Y)=X^2-Y^2=mn
(X^2-Y^2)^2=X^4+Y^4-2X^2Y^2=M^2N^2