求值：lg5²+lg2*lg50+(lg2)²答案写；2lg5+lg2*lg(5*10)+(lg2)_数学解答

求值：lg5²+lg2*lg50+(lg2)²
答案写；2lg5+lg2*lg(5*10)+(lg2)²①=2lg5+lg2*lg5+lg2+(lg2)² ②=2lg5+lg2*(lg5+lg2)+lg2③ .
第 ②步怎么得到的怎么就变成了lg2*lg5+lg2?

人气：306 ℃　时间：2020-02-10 04:28:51

解答

lg5²+lg2*lg50+(lg2)²
=2lg5+lg2*lg(5*10)+(lg2)²
=2lg5+lg2*(lg5+lg10)+(lg2)²
=2lg5+lg2*(lg5+1)+(lg2)²
=2lg5+lg2*lg5+lg2+(lg2)²
=2lg5+lg2+[lg2*lg5+(lg2)²]
=2lg5+lg2+lg2*(lg5+lg2)
=2lg5+lg2+lg2
=2(lg5+lg2)
=2