a = √3 + √2 হলে, (a6 -1)/a3 এর মান কত?
A 12√2
B 28√2
C 14√2
D 22√2
Solution
Correct Answer: Option D
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