Answer দেওয়া আছে,
` a = sqrt(6) + sqrt(5)`
`:. 1/a = 1/(sqrt(6) + sqrt(5))` [ব্যস্তকরণ করে]
`= (sqrt(6) - sqrt(5))/((sqrt(6) + sqrt(5)) (sqrt(6) - sqrt(5)))`
[লব ও হরকে `sqrt(6) - sqrt(5)` দ্বারা গুণ করে]
`= (sqrt(6) - sqrt(5))/((sqrt(6))^2 - (sqrt(5)^2))`
`= (sqrt(6) - sqrt(5))/(6 - 5)`
`= sqrt(6) - sqrt(5)`
:. `a - 1/a = sqrt(6) + sqrt(5) - (sqrt(6) - sqrt(5))`
`= sqrt(6) + sqrt(5) - sqrt(6) + sqrt(5)`
`= 2sqrt(5)`
প্রদত্ত রাশি, `= (a^6 - 1)/a^3`
`= a^6/a^3 - 1/a^3`
`= a^3 - 1/a^3`
`= (a - 1/a)^3 + 3a.1/a (a - 1/a)` [সূত্র প্রয়োগ করে]
`= (a - 1/a)^3 + 3(a - 1/a)`
`= (2sqrt(5))^3 + 3. 2sqrt(5)`
`= 8. 5sqrt(5) + 6sqrt(5)`
`= 40sqrt(5) + 6sqrt(5)`
`= 46sqrt(5)` (Ans)