Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 85532 by oustmuchiya@gmail.com last updated on 22/Mar/20

Find the term independent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Answered by mind is power last updated on 22/Mar/20

(2a−(1/(2a)))^k   =Σ_(i=0) ^k C_k ^i (2a)^i .(−(1/(2a)))^(k−i)   =Σ_(i=0) ^k C_k ^i (−1)^(k−i) 2^(2i−k) .a^(2i−k)   inedependsnt a⇒k=2i  9 not possible

$$\left(\mathrm{2}{a}−\frac{\mathrm{1}}{\mathrm{2}{a}}\right)^{{k}} \\ $$$$=\underset{{i}=\mathrm{0}} {\overset{{k}} {\sum}}{C}_{{k}} ^{{i}} \left(\mathrm{2}{a}\right)^{{i}} .\left(−\frac{\mathrm{1}}{\mathrm{2}{a}}\right)^{{k}−{i}} \\ $$$$=\underset{{i}=\mathrm{0}} {\overset{{k}} {\sum}}{C}_{{k}} ^{{i}} \left(−\mathrm{1}\right)^{{k}−{i}} \mathrm{2}^{\mathrm{2}{i}−{k}} .{a}^{\mathrm{2}{i}−{k}} \\ $$$${inedependsnt}\:{a}\Rightarrow{k}=\mathrm{2}{i} \\ $$$$\mathrm{9}\:{not}\:{possible} \\ $$

Commented by jagoll last updated on 23/Mar/20

yes sir. i got same result.   nothing independent term of x

$$\mathrm{yes}\:\mathrm{sir}.\:\mathrm{i}\:\mathrm{got}\:\mathrm{same}\:\mathrm{result}.\: \\ $$$$\mathrm{nothing}\:\mathrm{independent}\:\mathrm{term}\:\mathrm{of}\:\mathrm{x} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com