Question:` a = sqrt(6) + sqrt(5)` হলে `(a^6 - 1)/a^3` এর মান নির্ণয় কর। 

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) 

+ Report
Total Preview: 4493
` a = sqrt(6) + sqrt(5)` hole `(a^6 - 1)/a^3` ar man nirony karo.
Copyright © 2025. Powered by Intellect Software Ltd