Question

已知a+b=(lg2)^3+(lg5)^3+3lg2乘以lg5求a^3+b^3+3ab

Answer 1

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