x2- √5x + 1 = 0 হলে x5+ 1/x5এর মান কত?

x² - √5x + 1 = 0
বা, x² + 1 = √5x
বা, (x² +1)/x = √5
বা, x + 1/x = √5

x⁵ + 1/x⁵
= (x² + 1/x²)(x³ + 1/x³) - (x + 1/x)
= {(x + 1/x)² - 2.x.1/x}{(x + 1/x)³ - 3.x.1/x(x + 1/x)} - (x + 1/x)
= {(√5)² - 2}{(√5)³ - 3.√5} - √5
= 3 × 2√5 - √5
= 6√5 - √5
= 5√5