(lg5)^2+lg2xlg50 有三种方法 把lg50拆成 lg5+lg10 或 lg25+lg2 或lg100/2
1个回答

(lg5)²+lg2lg50

=(lg5)²+lg2(lg5+lg10)

=(lg5)²+lg2lg5+lg2

=lg5(lg5+lg2)+lg2

=lg5+lg2=1

(lg5)²+lg2lg50

=(lg5)²+lg2(lg25+lg2 )

=(lg5)²+2lg2lg5+(lg2)²

=(lg5+lg2)²=1

(lg5)²+lg2lg50

=(lg5)²+lg2lg100/2

=(lg5)²+lg2(lg100-lg2)

=(lg5)²+lg2(2-lg2)

=(lg5)²-(lg2)²+2lg2

=(lg5+lg2)(lg5-lg2)+2lg2

=lg5-lg2+2lg2

=lg5+lg2=1