p2 - (√5)p + 1 = 0 হয়, তবে p3 + (1/p3) এর মান কত?

p² - (√5)p + 1 = 0 হয়, তবে p³ + (1/p³) এর মান কত?

A 5

C √5

D 2√5

Solution

Correct Answer: Option D

দেওয়া আছে,
p² - (√5)p + 1 = 0
বা, p² + 1 = (√5)p
বা, (p² + 1)/p = √5
বা, (p²/p) + (1/p) = √5
∴ p + (1/p) = √5

এখন,
p³ + (1/p³)= {p+ (1/p)}³ - [3 ⋅ p ⋅ (1/p) ⋅ {p + (1/p)}]
= (√5)³ - (3 ⋅ 1 ⋅ √5)
= 5√5 - 3√5
= 2√5

Solution

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