Question

已知2的a次幂加2的负a次幂=3,求8的a次幂加8的负a次幂

Answer 1

设2^a=A

2^a+2^-a=3 A+1/A=3

(A+1/A)^3=3^3

A^3+3A+3/A+1/A^3=27

A^3+1/A^3=27-3(A+1/A) A+1/A=3

A^3+1/A^3=27-3*3 2^a=A

(2^a)^3+1/(2^a)^3=18

8^a+8^-a=18