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I f space t h e space t e r m space f r e e space f r o m space x space i n space t h e space e x p a n s i o n space o f space left parenthesis square root of x minus k over x squared right parenthesis to the power of 10 space i s space 405 comma space f i n d space t h e space v a l u e space o f space k ?

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Asked by Topperlearning User 8th October 2016, 2:54 PM
Answered by Expert
Answer:

L e t space left parenthesis r plus 1 right parenthesis to the power of t h end exponent space t e r m space b e space t h e space f r e e space t e r m space t h e n
T subscript r plus 1 end subscript equals C presuperscript 10 subscript r x to the power of r over 2 end exponent open parentheses fraction numerator negative k over denominator x squared end fraction close parentheses to the power of 10 minus r end exponent
f o r space T subscript r plus 1 space end subscript t o space b e space i n d e p e n d e n t space o f space x comma space p o w e r space o f space x space s h o u l d space b e space 0 space s o
r over 2 minus left parenthesis 20 minus 2 r right parenthesis equals 0
5 r equals 40
r equals 8
T subscript 9 equals C presuperscript 10 subscript 8 k squared equals 405
fraction numerator 10.9 over denominator 2 end fraction k squared equals 405
k squared equals 810 over 90
k equals plus-or-minus 3

Answered by Expert 8th October 2016, 4:54 PM
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