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

Question

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

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Natalia 2 months 2021-12-03T07:13:39+00:00 1 Answer 0 views 0

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    2021-12-03T07:15:24+00:00

    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 

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