先化简再求值x分之1+x除(x-(1+x平方)⼀x平方),其中x=根号2加1

2024-12-01 02:46:14
推荐回答(2个)
回答1:

x分之1+x除(x-(1+x平方)/x平方)
=1/x+x/[x-(1+x^2)/x^2]
=1/x+x/(x-1/x^2-1)
=(x-1/x^2-1+x^2)/(x^2-1/x-x)
=[(x-1)+(x+1/x)(x-1/x)] / [x(x-1)-1/x]
x值比较特殊, x=√2+1, 所以x的倒数1/x=√2-1
这样代入的时候就是比较容易求值了
=[√2+2√2.2] / [(√2+1).√2-(√2-1)]
=5√2 / (2+√2-√2+1)
=5√2 / 3

回答2:

5^(0.5)/3