作业帮 > 数学 > 作业

化简(8+2根号5-根号10-根号6)/(根号5+根号3-根号2)

来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/11/10 12:17:15
化简(8+2根号5-根号10-根号6)/(根号5+根号3-根号2)
分子上是根号15,
化简(8+2根号5-根号10-根号6)/(根号5+根号3-根号2)
[8 + 2(15)^(1/2) - (10)^(1/2) - 6^(1/2)]/[5^(1/2) + 3^(1/2) - 2^(1/2)]
= {3 + 2(15)^(1/2) + 5 - 2^(1/2)[5^(1/2) + 3^(1/2)]}/[5^(1/2) + 3^(1/2) - 2^(1/2)]
= {[3^(1/2) + 5^(1/2)]^2 - 2^(1/2)[5^(1/2) + 3^(1/2)]}/[5^(1/2) + 3^(1/2) - 2^(1/2)]
= [3^(1/2) + 5^(1/2)][3^(1/2) + 5^(1/2) - 2^(1/2)]/[5^(1/2) + 3^(1/2) - 2^(1/2)]
= 3^(1/2) + 5^(1/2)
---------------
分子上是根号15吧.