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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