.(x^2+y^2)(x^2+y^2-2008)=2009,求x^2+y^2的值

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.(x^2+y^2)(x^2+y^2-2008)=2009,求x^2+y^2的值
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.(x^2+y^2)(x^2+y^2-2008)=2009,求x^2+y^2的值
.(x^2+y^2)(x^2+y^2-2008)=2009,求x^2+y^2的值

.(x^2+y^2)(x^2+y^2-2008)=2009,求x^2+y^2的值
(x^2+y^2)(x^2+y^2-2008)=2009,
(x^2+y^2)^2-2008(x^2+y^2)-2009=0,
(x^2+y^2-2009)((x^2+y^2+1)=0,
x^2+y^2=2009,x^2+y^2=-1(舍去)
所以x^2+y^2=2009

就是换元法。 设x^2+y^2=t
则 t(t-2008)=2009
t^2-2008t-2009=0
解得t=-1 或t=2009.
但是t=x^2+y^2不可能为负数， 所以x^2+y^2=2009

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