x + (1/x) = √2 হলে, x⁴+(1/x)⁴ =?

প্রশ্ন: x + (1/x) = √2 হলে, x⁴+(1/x)⁴ =?

সমাধান:
দেওয়া আছে,
x + (1/x) = √2

এখন,
x⁴ + (1/x⁴)
= (x²)² + (1/x²)²
={x² + (1/x²)}² - 2 . x² . (1/x²)
= {x + (1/x)² - 2x . (1/x)}² - 2
= {(√2)² - 2}² - 2
= (2 - 2)² - 2
= 0² - 2
= 0 - 2
= - 2