CBSE Class 11-science Answered
Please solve this question
![question image](https://images.topperlearning.com/topper/new-ate/13027265106351141IMG20180622WA0000.jpg)
Asked by vikasg13.hardware | 23 Jun, 2018, 17:46: PM
{x}, [x], x are in geometric progression
Let they are a, ar, ar2
Hence, {x} = x - [x]
a = ar2 - ar
r2 - r - 1 = 0
r =
using formula
![begin mathsize 16px style fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/0ab280efcab6a1e0ef6ca91b9a7bca30.png)
r = ![begin mathsize 16px style fraction numerator 1 plus square root of 5 over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/d5964e589a272b4e98b1cc00bde2ad93.png)
![begin mathsize 16px style fraction numerator 1 plus square root of 5 over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/d5964e589a272b4e98b1cc00bde2ad93.png)
ar = [x] = k (say)
a = ![begin mathsize 16px style fraction numerator 2 straight k over denominator square root of 5 plus 1 end fraction equals fraction numerator straight k open parentheses square root of 5 minus 1 close parentheses over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/9cc4021881f34547e78945b2ffed5644.png)
![begin mathsize 16px style fraction numerator 2 straight k over denominator square root of 5 plus 1 end fraction equals fraction numerator straight k open parentheses square root of 5 minus 1 close parentheses over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/9cc4021881f34547e78945b2ffed5644.png)
a = {x} lies in [0, 1)
![begin mathsize 16px style 0 less than fraction numerator straight k open parentheses square root of 5 minus 1 close parentheses over denominator 2 end fraction less than 1
0 less than straight k less than fraction numerator 2 over denominator square root of 5 minus 1 end fraction equals fraction numerator square root of 5 plus 1 over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/57e4c4c55cd45b835e80073686685b6e.png)
k = 1
r = ![begin mathsize 16px style fraction numerator square root of 5 plus 1 over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/2bcac9a9724f7b371cb110756f92a93d.png)
![begin mathsize 16px style fraction numerator square root of 5 plus 1 over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/2bcac9a9724f7b371cb110756f92a93d.png)
xn = (ar2 )n =
>100
![begin mathsize 16px style open parentheses fraction numerator square root of 5 plus 1 over denominator 2 end fraction close parentheses to the power of straight n end style](https://images.topperlearning.com/topper/tinymce/cache/d70b8a67c8445396b1753e531a33032a.png)
![begin mathsize 16px style fraction numerator square root of 5 plus 1 over denominator 2 end fraction equals fraction numerator 2.23 plus 1 over denominator 2 end fraction equals 1.6 end style](https://images.topperlearning.com/topper/tinymce/cache/289af4bcd2aea2c599f2a7ce04173cc7.png)
1.6n > 100
Using logarithm we can say that n = 10
Answered by Sneha shidid | 27 Jun, 2018, 09:20: AM
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