Question

已知a+b=(lg2)的立方+(lg5)的立方+3lg2lg5,求a的立方+b的立方+3ab的值

Answer 1

1

a+b=(lg2)^3+(lg5)^3+3(lg2)*(lg5)

=[(lg2)+(lg5)][(lg2)^2-(lg2)*(lg5)+(lg5)^2]+3(lg2)*(lg5)

=1*[(lg2)^2-(lg2)*(lg5)+(lg5)^2]+3(lg2)*(lg5)

=[(lg2)+(lg5)]^2-3(lg2)*(lg5)+3(lg2)*(lg5)

=1

a^3+b^2+3ab

=(a+b)[(a+b)^2-3ab]+3ab

=1*(1^2-3ab)+3ab

=1