(1^4+1/4)*(3^4+1/4)*.(19^4+1/4)/(2^4+1/4)*(4^4+1/4).(20^4+1/4)等于多_数学解答

(1^4+1/4)*(3^4+1/4)*.(19^4+1/4)/(2^4+1/4)*(4^4+1/4).(20^4+1/4)等于多少
(1^4+1/4)*(3^4+1/4)*.(19^4+1/4)/(2^4+1/4)*(4^4+1/4).(20^4+1/4)这个怎么样计算啊,
怎么样计算呢,有什么简单的方法,这是在分式的通分这一节出的题目.大家帮想下,谢了

人气：148 ℃　时间：2020-03-27 20:37:36

解答

x^4+1/4=x^4+x^2+1/4-x^2=(x^2+1/2)^2-x^2)=(x^2+1/2+x)(x^2+1/2-x)=(x+1/2)^2+1/4)(x-1/2)^2+1/4)即得x^4+1/4=(x+1/2)^2+1/4)(x-1/2)^2+1/4)(1^4+1/4)*(3^4+1/4)*.(19^4+1/4)/(2^4+1/4)*(4^4+1/4).(20^4+1/4)={((1/...