lg[√(3+√5)+√(3-√5)]

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/26 10:41:47
lg[√(3+√5)+√(3-√5)]lg[√(3+√5)+√(3-√5)]lg[√(3+√5)+√(3-√5)]令a=√(3+√5)b=√(3-√5)则ab=√(9-5)=2a²+b

lg[√(3+√5)+√(3-√5)]
lg[√(3+√5)+√(3-√5)]

lg[√(3+√5)+√(3-√5)]
令a=√(3+√5)
b=√(3-√5)
则ab=√(9-5)=2
a²+b²=(3+√5)+(3-√5)=6
则(a+b)²
=a²+b²+2ab
=6+4
=10
所以原式=lg(a+b)
=lg√10
=1/2*lg10
=1/2

因为:
2lg[√(3+√5)+√(3-√5)]
=lg[√(3+√5)+√(3-√5)]²
=lg[3+√5+3-√5+2√(9-5)]
=lg[6+4]
=lg10
=1
所以:
lg[√(3+√5)+√(3-√5)]=1/2