What will be the Mean? If

The mean of x and 1/x is M. Then the mean of x2 and 1/x2 is:

  1. M2                                                              
  2. M2-2
  3. 4M2-2
  4. 2M2-1
Monis Rasool Professor Asked on 7th July 2015 in Maths.
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1 Answer(s)

Answer: (4) 2M2 – 1
Explanation:-
Given-
(x + 1/x)/2 = M
Then, x + 1/x = 2M             …………………. (1)
Square on both side of equation (1)
(x + 1/x)2 = x2 + 1/x2 + 2 x X x 1/X
(2M)2 = x2 + 1/x2 + 2             {from equation (1) x + 1/x = 2M }
4M2 = x2 + 1/x2 + 2
4M2 – 2 = x2 + 1/x2
mean of x2 + 1/x2)/2 = (4M2 – 2)/2
= 2M2 – 1

Hence, the answer is (4) 2M2 – 1.

Anurag Mishra Professor Answered on 8th July 2015.
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