已知x+y=5,xy=2求x^8+y^8的值

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已知x+y=5,xy=2求x^8+y^8的值
已知x+y=5,xy=2求x^8+y^8的值

已知x+y=5,xy=2求x^8+y^8的值
x^2+y^2=(x+y)^2-2xy=21,x^4+y^4=(x^2+y^2)^2-2X^2y^2=433,x^8+y^8=(x^4+y^4)-2x^4y^4=187457

x^8+y^8
=(x^4+y^4)^2-2x^4y^4
=[(x^2+y^2)^2-2x^2y^2]-2(xy)^4
=[(x^2+y^2)^2-2(xy)^2]-2*2^4
=[(x^2+y^2)^2-2*2^2]-32
=[(x^2+y^2)^2-8]-32
=(x^2+y^2)^2-40
=(x+y)^2-2xy-40
=5^2-2*2-40
=25-44
=-19

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