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

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

(x - 1/x)² = (x + 1/x)² - 4x.1/x
(x - 1/x)² = (√5)² - 4
= 5 - 4
= 1
x - 1/x = 1

x² - 1/x² = (x + 1/x)(x - 1/x)
= √5 .1
= √5