实数a-b满足a^3+b^3+3ab=1 则a+b=多少
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实数a-b满足a^3+b^3+3ab=1 则a+b=多少
实数a-b满足a^3+b^3+3ab=1 则a+b=多少
实数a-b满足a^3+b^3+3ab=1 则a+b=多少
a^3+b^3+3ab=1
(a+b)(a^2-ab+b^2)+3ab=1
(a+b)[(a+b)^2-3ab]+3ab=1
(a+b)^3-3ab(a+b-1)=1
(a+b)^3-1=3ab(a+b-1)
(a+b-1)[(a+b)^2+(a+b)+1]=3ab(a+b-1)
a+b=1
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