Find the
mean
of
X-1, x,x+1
Answers
eASy very easy ty it out
Step-by-step explanation:
As, far as i understand the question, it asks for “what is x^2 and 1/ x^2” i.e it aims at finding the individual values of x^2 and 1/x^2. So, then hope the algebric method helps.
And if the mean of the given quantities is required it will be={[ 2M^2-2M (M^2-1)^(1/2)-1]+[2M^2+2M (M^2-1)^(1/2)-1]}/2= 2M^2-1.
(It is not that x^2 and 1/x^2 share the same values.When x^2 has the value with its root part negative i.e -2M (1-M^2)^(1/2), then 1/x^2 has value with root part positive i.e +2M (1-M^2)^(1/2), and vice versa).
So, if x=1, the means of (x^2,1/x^2) and that of (x,1/x) are equal maybe.
But say x=2.
Then mean of x and 1/x is (x+1/x)/2=(2+1/2)/2=1.25
And mean of x^2 and 1/x^2 is (4+1/4)/2=2.125..(i) not equal to 1.25 i.e mean of x and 1/x.
So. When x=2, mean of x and 1/x =1.25=M
By,obtained formula, mean of x^2 and 1/x^2=(2M^2-1)=(2*(1.25^2)-1)=2.125 equals (i).
So,hope the algebra is correct.
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Jaspreet Kaur, studied at Bachelor of Education Degrees
Answered June 23, 2017
Don't get into the algebra for this answer as this is a simple one and can be understood by assuming values of x… to make it more simple let us assume the value of x be 1(one).
Now, if mean of x and 1/x is M
=> Mean of 1 and 1/1 is 1 ( because we assumed value of x to be 1)
=> Mean of 1 and 1 is 1.
Now mean of x^2 and 1/x^2 will also be equal to 1 ( again because we assumed x= 1)
Conclusion is ( x and 1/x) & ( x^2 and 1/x^2 ) both will have same means….
:-)
3.7K viewsView 9 Upvoters
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Seshadri Kesavan, BE CSE from Madras Institute of technology
Updated April 8, 2018 · Author has 472 answers and 963.9K answer views
Mean of x and 1/x is M. So,
(x+1/x)/2 = M
Squaring on both sides,
(x+1/x)²/2² = M²
(x² + 1/x² + 2×x×1/x)/4 = M²
x² + 1/x² + 2 = 4M²
x² + 1/x² = 4M² - 2
Dividing by 2 on both sides,
(x² + 1/x²)/2 = (4M² - 2)/2
=> (x² + 1/x²)/2 = 2×(2M² - 1)/2 = 2M² - 1
=> Mean of x² and 1/x² = (2M²-1)
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Krishan Rajdhari, Project Engineer at Rajdhari Constructions (2016-present)
Answered June 24, 2017 · Author has 552 answers and 928.2K answer views
If mean of x+1/x is M then the mean of x^2 +1/x^2 will always be 4(M^2) - 2 for any value of x.
(A+B)^2= A^2 +B^2 +2AB
(A+B)/2 = M or A+B= 2M on squaring both side, we get A^2+B^2+2AB =4M^2 or A2 +B2 =4M^2–2AB and mean of x^2+1/x^2=(4M^2–2)/2
Here A is x and B is 1/x
I hope you got it
Best of luck
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Umesh Prasad Singh
Answered August 17, 2020 · Author has 1.9K answers and 132.6K answer views
Mean of x and 1/x=(x+1/x)/2=M given
x+1/x=2M
Squaring both sides we have,
(x+1/x)^2=(2M)^2
=> x^2. + 2 x.1/x + 1/x^2 = 4M^2
=> x^2 + 1/x^2. = 4M^2 -2=2(M^2–1). Ans.
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Khaliquzzaman Khan, former Graduate Trained Teacher at Directorate of Education Port Blair (1978-2015)
Answered June 22, 2017 · Author has 604 answers and 285.9K answer views
Mean of x and 1/x is M implies that:
x + 1/x = 2M
squaring both side
x^2 + 1/ x^2 + 2 = 4 M^2
so x^2 + 1/ x^2 = 4 M^2 -2
x^2 + 1/ x^2 = 2(2M^2 -1)
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Ved Prakash Sharma, former Lecturer at Sbm Inter College, Rishikesh (1971-2007)
Answered October 19, 2018 · Author has 8.4K answers and 4.2M answer views
Mean of x and 1/x is M.
(x+1/x)/2==M
x+1/x=2M………….(1)
Mean of x^2 and 1/x^2 =(x^2+1/x^2)/2
= [(x+1/x)^2–2]/2
= (4M^2-2)/2.
= 2M^2 -1. Answer.