(lg5)^2+lg2*lg50 求值

分类: 作业答案 • 2021-12-19 12:07:37

问题描述：

(lg5)^2+lg2*lg50 求值

答

(lg5)²+lg2×lg50
=(lg5)²+lg2×(lg5+lg10)
=(lg5)²+lg2×lg5+lg2
=(lg5)×(lg5+lg2)+lg2
=lg5×1+lg2
=lg(5×2)
=1

答

=(lg5)^2+lg2*(lg5+1)
=(lg5)^2+(1-lg5)(1+lg5)
=(lg5)^2+1-(lg5)^2
=1