Question

a+√b+√c+√d/(-b)+(-c)+(-d)

Answer 1

问：a+√b+√c+√d/(-b)+(-c)+(-d)

答：首先将分母中的每个数取负号，并合并为一个负数，即：-b-c-d=-(b+c+d)然后将分子中的每个根式拆分为一对相同的根式，即：a+√b+√c+√d = a+2√b/2+2√c/2+2√d/2 = a+2√b·c·d/2·√b·c·d+2√c·d·b/2·√b·c·d+2√d·b·c/2·√b·c·d = a+2(√bcd/√bcd)(√bc+√cd+√db) = a+2√bcd/(√bcd)(√bc+√cd+√db) = a+2√bcd/(√b·d·c+√b·c·d+√d·b·c)最后，将分子、分母的结果带回原式中，即：a+2√bcd/(√b·d·c+√b·c·d+√d·b·c)/(-(b+c+d))= a-2√bcd/(√b·d·c+√b·c·d+√d·b·c)·(b+c+d)因此，原式的结果为：a-2√bcd/(√b·d·c+√b·c·d+√d·b·c)·(b+c+d)