x² - √6x + 1 = 0 হলে x² - (1/x)² এর মান কত?

দেওয়া আছে,
x² − √6x + 1=0
⇒ x² + 1 =√6x
⇒ x²/x + 1/x = √6
⇒ x + 1/x = √6

এখন
(x - 1/x)² = (x + 1/x)² - 4.x.1/x
(x - 1/x)² = (√6)² - 4
(x - 1/x)² = 6 - 4
(x - 1/x)² = 2
x - 1/x =√2

x² - (1/x)² = (x + 1/x)(x - 1/x)
= √6 × √2
= √12
= 2√3