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CBSE Class 11-science Answered

Please solve this question 
question image
Asked by vikasg13.hardware | 23 Jun, 2018, 05:46: PM
answered-by-expert Expert Answer
{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 = begin mathsize 16px style fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction end style using formula 
r = begin mathsize 16px style fraction numerator 1 plus square root of 5 over denominator 2 end fraction end style
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
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
 
 
k = 1
r = begin mathsize 16px style fraction numerator square root of 5 plus 1 over denominator 2 end fraction end style
xn  = (ar2 )n = 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>100
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
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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