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Find-the-term-indepent-of-x-in-the-expression-of-2x-1-2x-9-




Question Number 85418 by oustmuchiya@gmail.com last updated on 21/Mar/20
Find the term indepent of x in the expression of (2x−(1/(2x)))^9
$${Find}\:{the}\:{term}\:{indepent}\:{of}\:{x}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$
Commented by jagoll last updated on 22/Mar/20
let 2x= u  (u−(1/u))^3 = u^3 −3(u^2 )((1/u))+3u((1/u^2 ))−((1/u^3 ))  = u^3 −3u+(3/u)−(1/u^3 )  nothing term independent of x  similarly to (u−(1/u))^9
$$\mathrm{let}\:\mathrm{2x}=\:\mathrm{u} \\ $$$$\left(\mathrm{u}−\frac{\mathrm{1}}{\mathrm{u}}\right)^{\mathrm{3}} =\:\mathrm{u}^{\mathrm{3}} −\mathrm{3}\left(\mathrm{u}^{\mathrm{2}} \right)\left(\frac{\mathrm{1}}{\mathrm{u}}\right)+\mathrm{3u}\left(\frac{\mathrm{1}}{\mathrm{u}^{\mathrm{2}} }\right)−\left(\frac{\mathrm{1}}{\mathrm{u}^{\mathrm{3}} }\right) \\ $$$$=\:\mathrm{u}^{\mathrm{3}} −\mathrm{3u}+\frac{\mathrm{3}}{\mathrm{u}}−\frac{\mathrm{1}}{\mathrm{u}^{\mathrm{3}} } \\ $$$$\mathrm{nothing}\:\mathrm{term}\:\mathrm{independent}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{similarly}\:\mathrm{to}\:\left(\mathrm{u}−\frac{\mathrm{1}}{\mathrm{u}}\right)^{\mathrm{9}} \\ $$

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