Question

x^4 + 1/x^4 =119 then find x^5 - 1/x^5​

Answer 1

Answer:

x⁴ + 1/x⁴ = 119

=> x⁴ + 1/x⁴ + 2 = 121

=> (x² + 1/x²) ² = 11²

=> x² + 1/x² = 11    ,  ignore the negative value as LHS is +ve.

=> x² + 1/x² - 2 = 9

=> (x - 1/x)² = 3²

=> x - 1/x = +3 or -3

=> (x - 1/x)³ = x³ - 1/x³ - 3 x * 1/x * (x - 1/x)

      (+ 3) ³ = x³ - 1/x³ - 3 ( + 3)

Answer:      x³ - 1/x³ = 3³ + 9 or -30 - 9 = + 36