Find the value of the given equation:

x + 1/x =3, then the value of x5 + 1/x5 is

  1. 132
  2. 122
  3. 123
  4. 110
Anurag Mishra Professor Asked on 29th December 2015 in Maths.
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  • 1 Answer(s)

    Answer is 123 

    Explanation:-
    X + 1/X  = 3
    Square on both side,
    (X + 1/X)2 = 32
    X2  + 1/X2 + 2 X x 1/X = 9
    X2  + 1/X2 + 2 = 9
    X2  + 1/X2 = 9 – 2
    X2  + 1/X2 = 7  ………………………(1)

    Again, X + 1/X = 3
    Cube on both side,
    (X + 1/X)3 = 33
    X3 + 1/X3 + 3 x X x 1/X (X + 1/X) = 3 x 3 x 3
    X3 + 1/X3 + 3 x 3 = 27
    X3 + 1/X3 = 27 – 9
    X3 + 1/X3 = 18 …………………. (2)
    Equation (1) multiply by (2),
    (X2  + 1/X2) (X3 + 1/X3) = 7 x 18
    X2 x X3 + X2 x 1/X3 + X3 x 1/X2 + 1/X2 x X3 = 126
    X5 + 1/X + X + 1/X5 = 126
    X5 + 1/X5 + X + 1/X = 126
    X5 + 1/X5 + 3 = 126
    X5 + 1/X5 = 126 – 3
    X5 + 1/X5 = 123

    Then, the value of X5 + 1/X5 is 123.

    Hence, the correct answer is option (3) 123.

    Monis Rasool Professor Answered on 29th December 2015.
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