Question

已知2的x次方+2的(-x)次方=a(常数),求8的x次方+8的(-x)次方的值

Answer 1

2的x次方+2的(-x)次方=a

8的x次方+8的(-x)次方

=(2^x)^3+(2^-x)^3

=[2^x+2^(-x)][(2^x)^2-2^x*2^(-x)+(2^(-x))^2]

=a*[(2^x+2^(-x))^2-2*2^x*2^(-x)-2]

=a[a^2-2-2]

=a(a^2-4)

=a^3-4a