IF AVERAGE OF x AND 1/x IS 1, THEN 8x^10+4/x^5
Answers
Answer:
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….
:-)
Which is the best online supplement store for whey protein?
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)
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
If xx−1=2 , what is x?
What is x if xx=1/2 ?
If (x) ^2+(1/x) ^2=3, what is the value of x-(1/x)?
If −xx=−1, what is x?
If x+2x=1 then what is the value of x2+x+2x2(1−x) ?
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.
How has astrology changed your life?
I was a non-believer in astrology, but the testimony of my own life has made me change my thoughts on the subject. I come from a Hindu, middle-class family, my father was a government employee, and he ensured that our family always had enough. He would encourage me to do well in my studies
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)
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.
m square minus 2
2(M^2)-1
2
What is the meaning of x^3 and 1/x^3 if the mean of x and 1/x is m?
If mean of x,1/x is m, then what is the mean of x^3,1/x^3?
If x+1x−2=2 , what is x?
If x(x−1)2=1 , what is x?
If A^x=b^y=c^z and b^2=AC, then what is the value of y?
If xx−1=2 , what is x?
What is x if xx=1/2 ?
If (x) ^2+(1/x) ^2=3, what is the value of x-(1/x)?
If −xx=−1, what is x?
If x+2x=1 then what is the value of x2+x+2x2(1−x) ?
If 1x=2 what is x?
If 2^x = 3^y = 6^(-z), then what is the value of 1/x + 1/y + 1/z?
If 1/x + 2/y = 1/z and xy = z, then what is the average of x and y?
Why is 1/ (x^1/2) = (x^-1/2)?
If x2=2x , what is x?