怎么化简?感觉奇怪.就差1步{1/a}+{[√2×2^(x-1)]/a..给√2/2.怎么弄的?题目哪里不懂指出,a=(2^x+√2)

Question

怎么化简?感觉奇怪.就差1步
{1/a} + {[√2×2^(x-1)]/a..给 √2/2.怎么弄的?题目哪里不懂指出,
a=(2^x+√2)

Answer 1

{1/a} + {[√2×2^(x-1)]/a=1/a*(1+√2×2^(x-1))
=1/a*(1+2^(x-1+1/2))
=1/a*(1+2^(x-1/2))
=1/a*(1+2^x/√2)
=1/a*(2^x+√2)/√2
∵a=(2^x+√2)
∴1/a=1/(2^x+√2)
从而 1/a*(2^x+√2)/√2=1/(2^x+√2)*[(2^x+√2)/√2]
=1/√2
=√2/(√2*√2)
=√2/2