化简：根号5+根号3减根号2/8+2根号15+根号10减根号6_数学解答

化简：根号5+根号3减根号2/8+2根号15+根号10减根号6

人气：349 ℃　时间：2020-03-27 14:55:03

解答

[5^(1/2) + 3^(1/2) - 2^(1/2)]/[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)]/
=-1/[ 3^(1/2) + 5^(1/2)]