a = √3 + √2 হলে, (a6- 1)/a3এর মান কত?

প্রশ্ন: a = √3 + √2 হলে, (a⁶ - 1)/a³ এর মান কত?

সমাধান:
দেওয়া আছে, a = √3 + √2
∴ (1/a) = 1/(√3 + √2)
= (√3 - √2)/(√3 + √2)(√3 - √2)
= (√3 - √2)/(3 - 2)
= √3 - √2

∴ a - (1/a) = √3 + √2 - √3 + √2 = 2√2

এখন, (a⁶ -1)/a³ = (a⁶/a³) - (1/a³)
= a³ - (1/a³)
= {a - (1/a)}³ + 3 ⋅ a ⋅ (1/a){a - (1/a)}
= (2√2)³ + 3 ⋅ 2√2
= 8 ⋅ 2√2 + 6√2
= 22√2