Question

计算（x+1/x)(x2+1/x2)(x4+1/x4)…（x16+1/x16)(x2-1)

数字代表几次幂，1/x2读作x的二次幂分之一，请各位牛人帮忙呀

Answer 1

原式=（x+1/x)(x-1/x)(x^2+1/x^2)……(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^2-1/x^2)(x^2+1/x^2)(x^4+1/x^4)……(x^16+1/x^16)(x^2-1)/(x-1/x)
=……
=(x^16-1/x^16)(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^32-1/x^32)(x^2-1)/(x-1/x)
=(x^32-1/x^32)(x^2-1)/[(x^2-1)/x]
=x(x^32-1/x^32)
=x^33-1/x^31
x^33表示x的33次幂