log6[(根号下2+根号下3)+(根后下2-根号下3)]
问题描述:
log6[(根号下2+根号下3)+(根后下2-根号下3)]
题目是这样的
log6{[根号下(2+根号下3)]+[根后下(2-根号下3)]}
答
√(2+√3)=√[(4+2√3)/2]
=√[(3+2√3+1)/2]
=√[(√3+1)^2/2]
=(√3+1)*√(1/2)
同理√(2-√3)=(√3-1)*√(1/2)
所以真数=(√3+1)*√(1/2)+(√3-1)*√(1/2)
=2√3*√(1/2)
=√6
=6^(1/2)
所以原式=1/2