化简求值 (1g2)^3+(1g5)^3+3*1g2*1g5

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 12:13:11
化简求值 (1g2)^3+(1g5)^3+3*1g2*1g5

化简求值 (1g2)^3+(1g5)^3+3*1g2*1g5
化简求值 (1g2)^3+(1g5)^3+3*1g2*1g5

化简求值 (1g2)^3+(1g5)^3+3*1g2*1g5
(1g2)^3+(1g5)^3+3*1g2*1g5
=(lg2+lg5)[(lg2)²-lg2lg5+(lg5)²]+3lg2lg5
=lg10[(lg2)²-lg2lg5+(lg5)²]+3lg2lg5
=(lg2)²-lg2lg5+(lg5)²+3lg2lg5
=(lg2)²+2lg2lg5+(lg5)²
=(lg2+lg5)²
=(lg10)²
=1²
=1

那个15级是对的

(1g2)^3+(1g5)^3+31g2*1g5
=(lg2+lg5)[(lg2)^2+(lg5)^2-lg2lg5]+31g2*1g5
=[(lg2)^2+(lg5)^2-lg2lg5]+31g2*1g5
=[(lg2)^2+(lg5)^2+2lg2lg5]
=(lg2+lg5)^2
=1

前面回答的都正确