a = √6 + √5 হলে, (a6- 1)/a3এর মান কত?

প্রশ্ন: a = √6 + √5 হলে, (a⁶ - 1)/a³ এর মান কত?

সমাধান:
a = √6 + √5
এখন,
1/a = 1/(√6 + √5)
= (√6 - √5)/(√6 + √5)(√6 - √5)
= (√6 - √5)/(6 - 5)
= √6 - √5

∴ a - (1/a) = √6 + √5 - √6 + √5 = 2√5

(a⁶ - 1)/a³  = (a⁶/a³) - (1/a³)
= a³ - (1/a³)
= {(a - (1/a)}³ + 3 ⋅ a ⋅ (1/a) ⋅ {(a - (1/a)}
= (2√5)³ + 3 ⋅ 2√5
= 40√5 + 6√5
= 46√5