✔ 最佳答案
(1)
a³ˣ + a⁻³ˣ (aˣ)³ + (aˣ)⁻³
-------------- = -------------------
aˣ + a⁻ˣ aˣ + a⁻ˣ
(aˣ + a⁻ˣ)[(aˣ)² - (aˣ)(a⁻ˣ) + (aˣ)⁻²]
= -------------------------------------------- - - - - - - - - -→ 公式 : a³ + b³ = (a+b) (a² - ab + b²)
aˣ + a⁻ˣ
= a²ˣ - 1 + a⁻²ˣ
= 3 - 1 + 1/a²ˣ
= 2 + 1/3
= 7/3
~~~~~~~~~~~~~~~~~~~ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ~~~~~~~~~~~~~~~~~~~
(2)
a³ˣ - a⁻³ˣ (aˣ)³ - (aˣ)⁻³
-------------- = -------------------
aˣ - a⁻ˣ aˣ - a⁻ˣ
(aˣ - a⁻ˣ)[(aˣ)² + (aˣ)(a⁻ˣ) + (aˣ)⁻²]
= -------------------------------------------- - - - - - - - - -→ 公式 : a³ - b³ = (a-b) (a² + ab + b²)
aˣ - a⁻ˣ
= a²ˣ + 1 + a⁻²ˣ
= 2 + 1 + 1/a²ˣ
= 3 + 1/2
= 7/2
(3)
(aˣ + a⁻ˣ)² = (aˣ)² + 2(aˣ)(a⁻ˣ) + (a⁻ˣ)²
=> 3² = a²ˣ + 2 + a⁻²ˣ
=> a²ˣ + a⁻²ˣ = 7
a³ˣ + a⁻³ˣ (aˣ)³ + (aˣ)⁻³
∴ -------------- = -------------------
a²ˣ + a⁻²ˣ 7
(aˣ + a⁻ˣ)[(aˣ)² - (aˣ)(a⁻ˣ) + (aˣ)⁻²]
= ----------------------------------------... - - - - - - - - -→ 公式 : a³ + b³ = (a-b) (a² - ab + b²)
7
3 (a²ˣ - 1 + a⁻²ˣ)
= ------------------------
7
請等等 ......