已知x+y=-2+xy=4+求x^8+8y^5
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x+y=-2①
xy=4。②
①^2-4*②，得(x-y)^2=-12,
x-y=土2√3i,③
由①③解得(x,y)=(-1+√3i,-1-√3i),(-1-√3i,-1+√3i).
(-1土√3i)^2=-2干2√3i,
(-2干2√3i)^2=-8土8√3i,
当(x,y)=(-1+√3i,-1-√3i)时
x^8+8y^5
=(-8+8√3i)^2+8(-1-√3i)(-8-8√3i)
=(-8+8√3i)^2+(-8-8√3i)^2
=-256.
对另一种情况，值不变。
xy=4。②
①^2-4*②，得(x-y)^2=-12,
x-y=土2√3i,③
由①③解得(x,y)=(-1+√3i,-1-√3i),(-1-√3i,-1+√3i).
(-1土√3i)^2=-2干2√3i,
(-2干2√3i)^2=-8土8√3i,
当(x,y)=(-1+√3i,-1-√3i)时
x^8+8y^5
=(-8+8√3i)^2+8(-1-√3i)(-8-8√3i)
=(-8+8√3i)^2+(-8-8√3i)^2
=-256.
对另一种情况，值不变。
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