x - 2 = √3 হলে x⁴ + 1/x⁴ এর মান কত?

প্রশ্ন: x - 2 = √3 হলে x⁴ + 1/x⁴ এর মান কত?

সমাধান:
x - 2 = √3
x = √3 + 2
1/x = 1/(√3 + 2)
1/x = (2 - √3)/(√3 + 2) (2 - √3)
1/x = (2 - √3)/{2² - (√3)²}
1/x =(2 - √3)/(2 - 3)
1/x = 2 - √3

x + 1/x = 2 + √3 + 2 - √3 = 4

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
= {4² - 2}² - 2
= (16 - 2)² - 2
= 14² - 2
= 196 - 2
= 194