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

দেয়া আছে,
a = √7 + √6
1/a = 1/√7 + √6
=(√7 - √6)/(√7 + √6)(√7 - √6)
= (√7 - √6)/{(√7)² - (√6)²}
= (√7 - √6)/(7 - 6)
= (√7 - √6)/1
=√7 - √6

a - 1/a = √7 + √6 - (√7 - √6)
= √7 + √6 - √7 + √6
= 2√6


(a⁶ - 1)/a³ = a⁶/a³ - 1/a³
= a³ - (1/a)³
= (a - 1/a)³ + 3a.1/a.(a - 1/a)
= (2√6)³ + 3.2√6
= 8.6√6 + 6√6
= 48√6 + 6√6
= 54√6