x² - 4x - 1 = 0 হলে, x² + (1/x²) + 3x - (3/x) =?

প্রশ্ন: x² - 4x - 1 = 0 হলে, x² + (1/x²) + 3x - (3/x) =?

সমাধান:
x² - 4x - 1 = 0
⇒ x² - 1 = 4x
⇒ (x² - 1)/x = 4x/x
∴ x - (1/x) = 4

x² + (1/x²) + 3x - (3/x)
= (x - 1/x)² + 2.x.1/x + 3(x - 1/x)
= 4² + 2 + 3 × 4
= 16 + 2 + 12
= 30