已知a+b=(lg2)^3+(lg5)^3+3lg2*lg5,求a^3+b^3+3ab的值

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已知a+b=(lg2)^3+(lg5)^3+3lg2*lg5,求a^3+b^3+3ab的值
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已知a+b=(lg2)^3+(lg5)^3+3lg2*lg5,求a^3+b^3+3ab的值
已知a+b=(lg2)^3+(lg5)^3+3lg2*lg5,求a^3+b^3+3ab的值

已知a+b=(lg2)^3+(lg5)^3+3lg2*lg5,求a^3+b^3+3ab的值
a+b=(lg2)^3+(lg5)^3+3lg2*lg5
=(lg2+lg5)[(lg2+lg5)^2-3lg2*lg5]+3lg2*lg5=1-3lg2*lg5+3lg2*lg5=1(因为lg10=1)
a^3+b^3+3ab=(a+b)[(a+b)^2-3ab]+3ab=1