当x=4是,代数式(x-1)/(x的3/4次幂+x1/2次幂)*x的1/2次幂+x的1/4次幂/x的1/2次幂+1*x的1/4次幂+1的值是?

题目

当x=4是,代数式(x-1)/(x的3/4次幂+x1/2次幂)*x的1/2次幂+x的1/4次幂/x的1/2次幂+1*x的1/4次幂+1的值是?

答案

(x-1)/(x的3/4次幂+x1/2次幂)*(x的1/2次幂+x的1/4次幂)/(x的1/2次幂+1)*(x的1/4次幂+1)
=[(x^1/2-1)(x^1/2+1)/x^1/2*(x^1/4+1)]*[x^1/4*(x^1/4+1)/(x^1/2+1)(x^1/4+1)]
=(x^1/2-1)/[x^1/4*(x^1/4+1)]
=(x^1/4-1)(x^1/4+1)/[x^1/4(x^1/4+1)]
=(x^1/4-1)/x^1/4
=1-1/x^1/4
=1-1/4^1/4
=1-1/√2
=1-√2/2