Math, asked by preetisingh323, 1 year ago

if x+1/x=6, findx4+1/x4


Ls18: i ve done it but can u tell me how to upload the solution pictures
preetisingh323: yes at the left bottom pictures uploading option is there
Ls18: can't find it can u send me the screen shot
preetisingh323: let me try

Answers

Answered by Prakhar2908
7

Given,



x+\frac{1}{x}= 6



To find,



 {x}^{4}+\frac{1}{ {x}^{4} }



Main solution :



Using identity (a+b)^2=a^2+b^2+2ab



{(x+\frac{1}{x})}^{2}={x}^{2}+\frac{1}{{x}^{2}}+2



 {6}^{2}={x}^{2}+\frac{1}{ {x}^{2} } + 2



 {x}^{2}+\frac{1}{ {x}^{2} }=36 - 2



 {x}^{2}+\frac{1}{ {x}^{2} }=34



Whole squaring both sides.



Using identity (a+b)^2=a^2+b^2+2ab



 {( {x}^{2}+\frac{1}{{x}^{2} })}^{2}={x}^{4}+\frac{1}{{x}^{4}}+2



 {34}^{2}={x}^{4}+\frac{1}{{x}^{4}}+2



1156={x}^{4}+\frac{1}{{x}^{4} }+2



 {x}^{4}+\frac{1}{{x}^{4}}=1156-2



{x}^{4}+\frac{1}{{x}^{4}}=1154

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