jidianwu
幼苗
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x-y=2,x²+y²=4
x=2,y=0 是一组解;x=0,y=-2是另外一组解
x^2010+y^2010 = 2^2010
1年前
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是把x-y=2,x²+y²=4放在x的2010次方+y的2010次方里面算,求过程
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jidianwu
(x-y)²=x²+y²-2xy=2² => xy=0 (x²+y²)(x-y)=x³-y³+xy²-x²y=x³-y³=8=2³ => x³-y³=2³ (x³-y³)(x-y)=x^4+y^4-x³y-xy³=x^4+y^4=2^4 => x^4+y^4=2^4 (x^4+y^4)(x-y)=x^5-y^5+x(y^4)-(x^4)y=x^5-y^5=2^5 => x^5-y^5=2^5 …… x^2009-y^2009=2^2009 x^2010+y^2010=2^2010