Question

已知2的n次方+2的负n次方=a,求下列代数式的值:8的n次方+8的负n次方

Answer 1

2^n+2^(-n)=a

两边立方得：

a^3=(2^n+2^(-n))^3=2^3n +3*2^(2n)*2^(-n)+3*2^n*2^(-2n)+2^(-3n)

=8^n+3*2^n+3*2^(-n)+8^(-n)

∴8^n+8^(-n)=a^3-3(2^n+2^(-n))=a^3-3a