a = √7 + √6 হলে, (a⁶ -1)/a³ এর মান কত?

প্রশ্ন: a = √7 + √6 হলে, (a⁶ -1)/a³ এর মান কত?

সমাধান:
দেওয়া আছে,
a = √7 + √6

∴ (1/a) = 1/(√7 + √6)
= (√7 - √6)/(√7 + √6)(√7 - √6)
= (√7 - √6)/(7 - 6)
= √7 - √6

∴ a - (1/a) = √7 + √6 - √7 + √6 = 2√6

এখন,
(a⁶ -1)/a³
= (a⁶/a³) - (1/a³)
= a³ - (1/a³)
= {a - (1/a)}³ + 3 ⋅ a ⋅ (1/a){a - (1/a)}
= (2√6)³ + 3 ⋅ 2√6
= 8 ⋅ 6√6 + 6√6
= 54√6