Question

please solve fast.. ✌✌​

Answer 1

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 

Answer 2

$<font color =red>$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

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