Question

计算：(x+1/x)(x的平方+1/x的平方)(x的4次方+1/x的4次方)(x的8次方+1/x的8次方)(x的16次方

Answer 1

原式=(x-1/x)(x+1/x)(x的平方+1/x的平方)(x的4次方+1/x的4次方)(x的8次方+1/x的8次方)(x的16次方+1/x的16次方)(x的平方-1) /(x-1/x)

=(x^2-1/x^2)(x^2+1/x^2).(x^2-1)/(x-1/x)

=(x^4-1/x^4)(x^4+1/x^4).(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