p = √3 + √2, 1/p = √3 - √2 হলে, (p6 - 1)/p3 এর মান কত?

A 2√2

B  10√2 

C  22√2

D 14√2

Solution

Correct Answer: Option C

দেওয়া আছে,
p = √3 + √2
1/p = √3 - √2

∴ {p - (1/p)} = √3 + √2 - √3 + √2
                   = 2√2

এখন,
(p6 - 1)/p3
= (p6/p3) - (1/p3)
= p3 - (1/p3)
= {p - (1/p)}3 + [{3 × p × (1/p)} × {p - (1/p)}]
= (2√2)3 + (3 × 1 × 2√2)
= 16√2 + 6√2
= 22√2

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