Question

Se $2^{x} + 2^{-x} = a$ determine o valor de $8^{x} + 8^{-x}$

Answer 1

Olá,

(2ˣ+2⁻ˣ)³ = 2⁻³ˣ + 3·2⁻ˣ + 3·2ˣ + 2³ˣ = a³
(2³ˣ+2⁻³ˣ)+3·(2ˣ+2⁻ˣ) = a³
(2³)ˣ+(2³)⁻ˣ+3·(a) = a³
(8)ˣ+(8)⁻ˣ+3a = a³
8ˣ+8⁻ˣ = a³-3a

Resposta:

a³-3a