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In the expansion of $(2x+\frac{k}{x})^8$, where k is a positive constant, the constant is 700000. Find k.

 Dec 28, 2020
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We have  to  "cancel"  x's in the expansion

 

This will  happen  when we  have  the term

 

C (8,4)  (2x)^4  * ( k/x)^4    = 700000    simplify

 

70 * 2^4 * k^4   =  700000   divide out 70

 

70 * 16 * k^4  =  10000

 

16 * k^4 = 10000 

 

k^4  =  10000/16    take the positive 4th root

 

10/2  = k   =  5

 

 

cool cool cool

 Dec 28, 2020

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