(lg2)^3+(lg5)^3+lg5*lg8怎么算谢谢!
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(lg2)^3+(lg5)^3+lg5*lg8怎么算谢谢!
令a=lg2,b=lg5
则a+b=lg2+lg5=1
lg8=lg2^3=3lg2=3a
所以原式=a^3+b^2+3ab
=(a+b)(a^2-ab+b^2)+3ab
=1*(a^2-ab+b^2)+3ab
=a^2+2ab+b^2
=(a+b)^2
=1
则a+b=lg2+lg5=1
lg8=lg2^3=3lg2=3a
所以原式=a^3+b^2+3ab
=(a+b)(a^2-ab+b^2)+3ab
=1*(a^2-ab+b^2)+3ab
=a^2+2ab+b^2
=(a+b)^2
=1
(lg2)^3+(lg5)^3+lg5*lg8怎么算谢谢!
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