已知(x+y)^2n=1/8,(x-y)^n=4,求[(x+y)(x-y)]^4n的值

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已知(x+y)^2n=1/8,(x-y)^n=4,求[(x+y)(x-y)]^4n的值
已知(x+y)^2n=1/8,(x-y)^n=4,求[(x+y)(x-y)]^4n的值

已知(x+y)^2n=1/8,(x-y)^n=4,求[(x+y)(x-y)]^4n的值
(x+y)^(2n)=1/8,则:
(x+y)^(4n)=(1/8)²=1/64
(x-y)^n=4,则:
(x-y)^(4n)=4^4=64
则:
[(x+y(x-y)]^(4n)=[(x+y)^(4n)]×[(x-y)^(4n)]=1

(X+Y)^4n=(1/8)^2=1/64,
(X-Y)^4n=4^4n=64,
∴[(x+y)(x-y)]^4n=(X+Y)^4n*(X-Y)^4n=1/64*64=1

[(x+y)(x-y)]^4n
=(x+y)^4n(x-y)^4n
=[(x+y)^2n]^2*[(x-y)^n]^4
=(1/8)^2*4^4
=1/64*256
=4

(x+y)^4n=1/64
x-y)^4n=64
[(x+y)(x-y)]^4n=1