a² - 1 = √3a হলে (a⁶ - 1)/a³ = কত?

প্রশ্ন: a² - 1 = √3a হলে (a⁶ - 1)/a³ = কত?

সমাধান:
a² - 1 = √3a
(a² - 1)/a = √3a/a
a²/a - 1/a = √3
a - 1/a = √3

(a⁶ - 1)/a3
= a⁶/a³ - 1/a³
= a³ - 1/a³
= (a - 1/a)³ + 3a.1/a.(a - 1/a)
= (√3)³ + 3√3
= 3√3 + 3√3
= 6√3