2（lg√2)^2 +lg√2*lg5+(√(lg√2)^2-lg2+1)(lg√2)^2-lg2+1都是要开根号的·~_数学解答

2（lg√2)^2 +lg√2*lg5+(√(lg√2)^2-lg2+1)
(lg√2)^2-lg2+1
都是要开根号的·~

人气：360 ℃　时间：2020-01-27 12:18:34

解答

lg√2=(1/2)lg2
lg5=1-lg2
所以原式=2*(1/4)(lg2)^2+(1/2)lg2(1-lg2)+√[(1/4)*(lg2)^2-lg2+1]
=(1/2)(lg2)^2+(1/2)lg2-(1/2)(lg2)^2+(1/2))*√[(lg2)^2-4lg2+4]
=(1/2)lg2+(1/2)√(1-lg2)^2
=(1/2)lg2+(1/2)*(1-lg2)
=(1/2)lg2+(1/2)-(1/2)lg2
=1/2