x2- √2x + 1 = 0 হলে, x5+ 1/x5এর মান কত?

x² - √2x + 1 = 0
বা, x² + 1 = √2x
বা, (x² + 1)/x = √2
বা, x + 1/x = √2

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