作业帮已知m=(√2-1)负一次方+(√2+1)负一次方,那么(m-1)负一次方+(n+1)负一次方等于多少?
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/13 14:01:52
已知m=(√2-1)负一次方+(√2+1)负一次方,那么(m-1)负一次方+(n+1)负一次方等于多少?
答：
m=(√2-1)^(-1)+(√2+1)^(-1)
=1/(√2-1)+1/(√2+1)
=(√2+1)/[(√2+1)(√2-1)]+(√2-1)/[(√2-1)(√2+1)]
=(√2+1)/(2-1)+(√2-1)/(2-1)
=√2+1+√2-1
=2√2
(m-1)^(-1)+(m+1)^(-1)
=1/(m-1)+1/(m+1)
=(m+1+m-1)/(m²-1)
=2m/(m²-1)
=2*2√2/(8-1)
=4√2/7
m=(√2-1)^(-1)+(√2+1)^(-1)
=1/(√2-1)+1/(√2+1)
=(√2+1)/[(√2+1)(√2-1)]+(√2-1)/[(√2-1)(√2+1)]
=(√2+1)/(2-1)+(√2-1)/(2-1)
=√2+1+√2-1
=2√2
(m-1)^(-1)+(m+1)^(-1)
=1/(m-1)+1/(m+1)
=(m+1+m-1)/(m²-1)
=2m/(m²-1)
=2*2√2/(8-1)
=4√2/7