(1^4+1/4)(3^4+1/4).(19^4+1/4)/(2^4+1/4)*(4^4+1/4).(20^4+1/

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 18:45:49

(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

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)
={((1/2)^2+1/4)((3/2)^2+1/4)((5/2)^2+1/4)((7/2)^2+1/4)...((37/2)^2+1/4)((39/2)^2+1/4)}/{((3/2)^2+1/4)((5/2)^2+1/4)((7/2)^2+1/4)((9/2)^2+1/4)...((39/2)^2+1/4)((41/2)^2+1/4)}
=((1/2)^2+1/4)/((41/2)^2+1/4)=2/(41^2+1)=1/841

(1^4+1/4)*(3^4+1/4)*.(19^4+1/4)/(2^4+1/4)*(4^4+1/4).(20^4+1/ (（1^4+1/4)(3^4+1/4)(5^4+1/4).(19^4+1/4))/((2^4+1/4)(4^4+1/4) （1^4/4)(3^4+1/4)...(19^4+1\4) \ (2^4+1/4)(2^4+1/4)(4^4+1/4). 求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/ 计算：[1/4（1^4+3^4+5^4+……+19^4)]/[1/4(2^4+4^4+6^4+……+20^4)] 4 4 4 4 4=0 4 4 4 4 4=1 4 4 4 4 4=2 4 4 4 4 4=3 4 4 4 4 4=4 4 4 4 4=1 4 4 4 4=2 4 4 4 4=3 填标点符号 1/4,-3/4,-3/4,1/4,17/4,( ) 1/3,2/3,1/3,1/4,2/4,3/4,2/4,1/4,( ),( ),( ),( ),( ),( ),( ) (1四次方+1/4)(3四次方+1/4)..(19四次方+1/4)/(2四次方+1/4)(4四次方+1/4)...(20 求1/2*3+1/3*4+1/4*5+.+1/18*19+1/19*20 1/2×3+1/3×4+1/4×5+.+1/18×19+1/19×20等于?