Question

已知a+b=(lg2)^3+(lg5)^3+3lg2乘以lg5求a^3+b^3+3ab 今晚就要要详细过程，顺便说一下怎么做谢了

Answer 1

(a+b)=(lg2+lg5)^3-3*lg2*lg5*(lg2+lg5)+3lg2*lg5=1;
(a+b)^3=a^3+b^3+3ab(a+b) =a^3+b^3+3ab =1;
所以最终答案唯 1；

Answer 2

a+b=(lg2)^3+(lg5)^3+3lg2乘以lg5=（lg2+lg5)[(lg2)^2-lg2×lg5+(lg5)^2]+3lg2×lg5=1×[(lg2)^2-lg2×lg5+(lg5)^2]+3lg2×lg5=(lg2)^2-lg2×lg5+(lg5)^2+3lg2×lg5=(lg2+lg5)^2=1
a^3+b^3+3ab =1

Answer 3

a+b=(lg2)^3+(lg5)^3+3lg2lg5
=(lg2+lg5)^3-3(lg2)^2lg5-3lg2(lg5))^2+3lg2lg5
=1-3lg2lg5(lg2+lg5-1)
=1-3lg2lg5(1-1)
=1
a^3+b^3+3ab
=(a+b)^3-3a^2b-3ab^2+3ab
=1-3ab(a+b-1)
=1-3ab(1-1)
=1